CERCLES-02 kitcircle := S = (1/4)*a*b*c/R, e = sqrt(-a^2*c^2+c^4-b^2*c^2-a^2*b^2+a^4+b^4)/sqrt(a^2*b^2+a^2*c^2+b^2*c^2), {cos(omega) = (1/2)*(a^2+b^2+c^2)/sqrt(a^2*b^2+a^2*c^2+b^2*c^2), sin(omega) = (1/2)*a*b*c/(R*sqrt(a^2*b^2+a^2*c^2+b^2*c^2))}, r = (1/2)*c*b*a/((a+b+c)*R), s = (1/2)*a+(1/2)*b+(1/2)*c; NicvSSJTRzYiLCQqKkkiYUdGJSIiIkkiYkdGJUYpSSJjR0YlRilJIlJHRiUhIiIjRikiIiUvSSJlR0YlKiYsLiomRigiIiNGK0Y1Ri0qJEYrRi9GKSomRipGNUYrRjVGLSomRihGNUYqRjVGLSokRihGL0YpKiRGKkYvRikjRilGNSwoRjhGKUY0RilGN0YpI0YtRjU8JC8tSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2I0kmb21lZ2FHRiUsJComLCgqJEYoRjVGKSokRipGNUYpKiRGK0Y1RilGKUY8Rj1GOy8tSSRzaW5HRkJGRSwkKixGKEYpRipGKUYrRilGLEYtRjxGPUY7L0kickdGJSwkKixGK0YpRipGKUYoRiksKEYoRilGKkYpRitGKUYtRixGLUY7L0kic0dGJSwoRihGO0YqRjtGK0Y7 WW1:= sqrt(a^2*b^2+a^2*c^2+b^2*c^2); WW2:= sqrt(-a^2*c^2+c^4-b^2*c^2-a^2*b^2+a^4+b^4); WW3:= sqrt(a^6-a^4*b^2-a^4*c^2-a^2*b^4+3*a^2*b^2*c^2-a^2*c^4+b^6-b^4*c^2-b^2*c^4+c^6); WW4:= sqrt(b^3-b^2*c-b*c^2+c^3-a*b^2+3*a*b*c-a*c^2-a^2*b-a^2*c+a^3); KiQsKComSSJhRzYiIiIjSSJiR0YmRiciIiIqJkYlRidJImNHRiZGJ0YpKiZGKEYnRitGJ0YpI0YpRic= KiQsLiomSSJhRzYiIiIjSSJjR0YmRichIiIqJEYoIiIlIiIiKiZJImJHRiZGJ0YoRidGKSomRiVGJ0YuRidGKSokRiVGK0YsKiRGLkYrRiwjRixGJw== KiQsNiokSSJhRzYiIiInIiIiKiZGJSIiJUkiYkdGJiIiIyEiIiomRiVGKkkiY0dGJkYsRi0qJkYlRixGK0YqRi0qKEYlRixGK0YsRi9GLCIiJComRiVGLEYvRipGLSokRitGJ0YoKiZGK0YqRi9GLEYtKiZGL0YqRitGLEYtKiRGL0YnRigjRihGLA== KiQsNiokSSJiRzYiIiIkIiIiKiZJImNHRiZGKEYlIiIjISIiKiZGJUYoRipGK0YsKiRGKkYnRigqJkkiYUdGJkYoRiVGK0YsKihGMEYoRiVGKEYqRihGJyomRjBGKEYqRitGLComRiVGKEYwRitGLComRipGKEYwRitGLCokRjBGJ0YoI0YoRis=
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Equation cercle (d\303\251terminant \303\240 la Kimberling)</Font></Text-field> circ:= proc (x, y) options operator, arrow; [y^2+x^2, x, y, 1] end proc; Zio2JEkieEc2IkkieUdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlNyYsJiokOSUiIiMiIiIqJDkkRi5GL0YxRi1GL0YlRiVGJQ== Le principe du d\303\251terminant Matrix([circ(xi,eta), seq(circ(xi[j],eta[j]), j=1..3)]); #latexx(0), latexz(%); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKW9ydkM= matri:= Matrix([za,zb,zc]); mafac:= Diag(x+y+z,p1+q1+r1,p2+q2+r2,p3+q3+r3); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKWttUWQ= LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKHM1ZyY= magic:= Matrix(map( circ@op@bary2proj, [px,pp1,pp2,pp3])); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKStpYkI= SubMatrix(magic,1..4,2..4); FActor(mafac.%. (1/matri)); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKXdoKT4m LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKSlbcj0j matri4:= DiagonalMatrix([1, matri]); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKU9KUmI= tmp:= FActor(mafac.magic. (1/matri4)); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKVdMZj8= Row(tmp,1); LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSRyb3dHRig2Iy9JJCVpZEdGKCIpP3olZSU= tmp[1,1]*(x+y+z): collect(%, px, distributed); LC4qJiwmKiRJI3liRzYiIiIjIiIiKiRJI3hiR0YnRihGKUYpSSJ5R0YnRihGKSomLCYqJEkjeWNHRidGKEYpKiRJI3hjR0YnRihGKUYpSSJ6R0YnRihGKSomLCYqJEkjeWFHRidGKEYpKiRJI3hhR0YnRihGKUYpSSJ4R0YnRihGKSooLCYqJkYwRilGJkYpRigqJkYyRilGK0YpRihGKUYsRilGM0YpRikqKCwmKiZGOUYpRjJGKUYoKiZGN0YpRjBGKUYoRilGOkYpRjNGKUYpKigsJiomRiZGKUY3RilGKComRitGKUY5RilGKEYpRjpGKUYsRilGKQ== finafac:= <<-1, +ya^2+xa^2, yb^2+xb^2, yc^2+xc^2> | <<0|0|0>, mun>>; FActor(tmp.%): map(factor@simplify, collect(%, px, distributed), rule123); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKUspb2Ii LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKWN3ISlb FActor(mafac.magic. (1/matri4).finafac): (FActor@simplify)(%, rule123): subs(seq(seq( cat(k,j)=k[j], j=[1,2,3]), k=[p,q,r]), %); # latexx(mafac), latexy(matri4), latexy(finafac), latexz(%); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKWtzI1Ej
<Text-field style="Heading 1" layout="Heading 1">Equation cercle par centre et rayon</Text-field> basique : pythagore -pytha(pp,px)+rho2: tmp:= collect(%*(x+y+z)^2, rho2, factor); LCYqJkklcmhvMkc2IiIiIiwoSSJ4R0YlRiZJInlHRiVGJkkiekdGJUYmIiIjRiYqJixmcCosSSJjR0YlRitGKUYmSSJwR0YlRiZJInFHRiVGJkYqRiZGJioqSSJhR0YlRitGMUYmRipGK0YwRiYhIiIqKkYzRitGKEYmRjFGK0YqRiZGNCoqRjNGK0YoRitGMUYmSSJyR0YlRiZGJioqRjNGK0Y3RitGKUYmRihGJkY0KipGM0YrRilGJkYwRitGKkYmRiYqKkYzRitGKUYrRjBGJkY3RiZGNCoqSSJiR0YlRitGN0YrRilGJkYoRiZGNCoqRjxGK0YoRiZGMUYrRipGJkYmKipGPEYrRihGK0YxRiZGN0YmRjQqKEYvRitGKUYrRjBGK0Y0KihGL0YrRihGK0YxRitGNCosRi9GK0YoRiZGMUYmRipGJkYwRiZGJiosRi9GK0YxRiZGKkYmRjdGJkYoRiZGNCosRi9GK0YoRiZGMUYmRjdGJkYpRiZGJiosRi9GK0Y3RiZGKUYmRipGJkYwRiZGNCosRi9GK0YpRiZGMEYmRihGJkYxRiZGKyosRi9GK0YpRiZGMEYmRjdGJkYoRiZGJioqRi9GK0Y3RitGKUYmRihGJkYmKipGL0YrRilGJkYwRitGKkYmRjQqKkY8RitGMUYmRipGK0YwRiZGNCoqRjxGK0YpRiZGMEYrRipGJkY0KipGPEYrRilGK0YwRiZGN0YmRiYqKkYvRitGMUYmRipGK0YwRiZGJioqRi9GK0YoRiZGMUYrRipGJkY0KipGL0YrRihGK0YxRiZGN0YmRjQqKkYvRitGKUYrRjBGJkY3RiZGNCooRjNGK0Y3RitGKUYrRjQqKEYzRitGMUYrRipGK0Y0KixGM0YrRihGJkYxRiZGN0YmRilGJkYmKixGM0YrRihGJkYxRiZGKkYmRjBGJkY0KixGM0YrRjdGJkYpRiZGKkYmRjBGJkYmKixGM0YrRjdGJkYpRiZGMUYmRipGJkYrKixGM0YrRilGJkYwRiZGN0YmRihGJkY0KixGM0YrRilGJkYwRiZGMUYmRipGJkYmKihGPEYrRjdGK0YoRitGNCosRjNGK0YxRiZGKkYmRjdGJkYoRiZGJiosRjxGK0YoRiZGMUYmRjdGJkYpRiZGNCosRjxGK0YoRiZGMUYmRipGJkYwRiZGJiosRjxGK0Y3RiZGKUYmRipGJkYwRiZGJiosRjxGK0YpRiZGMEYmRjdGJkYoRiZGJiosRjxGK0YpRiZGMEYmRjFGJkYqRiZGNCooRjxGK0YqRitGMEYrRjQqLEY8RitGN0YmRihGJkYqRiZGMEYmRisqLEY8RitGMUYmRipGJkY3RiZGKEYmRiZGJiwoRjBGJkYxRiZGN0YmISIjRiY= -k*tmp+rho2*(x+y+z)^2+eqcircum(px)-(x+y+z)*ps(pu,px): {coeffs(expand(%), px)}: eli:= (factor@eliminate)(%, {k,u,v, w}); NyQ8Ji9JImtHNiIiIiIvSSJ1R0YmLCQqJiwsKihJInJHRiZGJ0kiYUdGJiIiI0kicUdGJkYnRicqKEkiY0dGJkYwRjFGJ0YuRichIiIqKEkiYkdGJkYwRjFGJ0YuRidGNComRjZGMEYuRjBGNComRjNGMEYxRjBGNEYnLChJInBHRiZGJ0YxRidGLkYnISIjRjQvSSJ2R0YmKiYsLCooRi9GMEY6RidGLkYnRicqKEY6RidGNkYwRi5GJ0Y0KihGM0YwRjpGJ0YuRidGJyomRjNGMEY6RjBGJyomRi9GMEYuRjBGJ0YnRjlGOy9JIndHRiYqJiwsKiZGL0YwRjFGMEYnKihGL0YwRjFGJ0Y6RidGJyooRjpGJ0YzRjBGMUYnRjQqJkY2RjBGOkYwRicqKEY2RjBGMUYnRjpGJ0YnRidGOUY7PCI= pp2uu:= unapply(subs(eli[1], pu), p,q,r)@OP; 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 eq_dou:= eqcircum(px)+rho2*(x+y+z)^2-ps(pu,px)*(x+y+z); LCwqKEkiYUc2IiIiI0kieUdGJSIiIkkiekdGJUYoRigqKEkiYkdGJUYmRilGKEkieEdGJUYoRigqKEkiY0dGJUYmRidGKEYsRihGKComSSVyaG8yR0YlRigsKEYsRihGJ0YoRilGKEYmRigqJkYxRigsKComSSJ1R0YlRihGLEYoRigqJkkidkdGJUYoRidGKEYoKiZJIndHRiVGKEYpRihGKEYoISIi test ok factor(subs(zipq(pu, pp2uu(pp)), eq_dou)-tmp);; #latexx(0),latexy(eq_dou), latexz(pp2uu(pp)); IiIh wolf:= (l*alpha+m*beta+n*gamma)*(a*alpha+b*beta+c*gamma)+(a*beta*gamma+b*gamma*alpha+c*alpha*beta):subs(alpha=x/a, beta=y/b, gamma=z/c, %): eq_wolf:= xcollect(%*a*b*c, [x+y+z], factor); LCoqJiwoKipJImxHNiIiIiJJInhHRidGKEkiYkdGJ0YoSSJjR0YnRihGKCoqSSJtR0YnRihJInlHRidGKEkiYUdGJ0YoRitGKEYoKipJIm5HRidGKEkiekdGJ0YoRi9GKEYqRihGKEYoLChGKUYoRi5GKEYyRihGKEYoKihGKyIiI0YpRihGLkYoRigqKEYqRjVGKUYoRjJGKEYoKihGL0Y1Ri5GKEYyRihGKA== R\303\250gle de calcul subs(zipq(px,pa), eq_wolf)/b/c; SSJsRzYi (eq_dou-eq_wolf)/(x+y+z): collect(factor(%), [x,y,z]): solve({coeffs}(%, px),{l,m,n}): subs(%, [l,m,n]); NyUqKCwmSSJ1RzYiISIiSSVyaG8yR0YmIiIiRilJImJHRiZGJ0kiY0dGJkYnKigsJkkidkdGJkYnRihGKUYpSSJhR0YmRidGK0YnKigsJkYoRilJIndHRiZGJ0YpRi9GJ0YqRic=
<Text-field style="Heading 1" layout="Heading 1">condilou, elimination des pp2uu</Text-field> evalms(pp2uu(pp)-pu): eli:= eliminate(%, {p,q}): tmp:= select(has,op(eli[2]),{v}); 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 (factor@subs)(zipq(pu,pp2uu(pp)), op(1,tmp)); (factor@subs)(zipq(pu,pp2uu(pp)), op(2,tmp)); collect(op(2,tmp), pu, factor, distributed): condilou:= xcollect(%,[rot3(a^2+b^2-c^2)]); LCQqKiwoKiRJImJHNiIiIiMhIiIqJEkiY0dGJ0YoRikqJEkiYUdGJ0YoIiIiRi4sKiomRi1GKEkicUdGJ0YuRi4qJkYxRi5GJkYoRikqJkYrRihGMUYuRikqJkkickdGJ0YuRiZGKCEiI0YuLCpGM0Y2KiZGNUYuRi1GKEYuRjRGKSomRjVGLkYrRihGKUYuLChJInBHRidGLkYxRi5GNUYuRjZGNg== IiIh LDAqJiwmKiZJImNHNiIiIiNJIndHRiciIiIhIiIqJkkidUdGJ0YqSSJ2R0YnRipGK0YqLCgqJEkiYUdGJ0YoRioqJEkiYkdGJ0YoRioqJEYmRihGK0YqRioqJiwmKiZGLUYqRjFGKEYrKiZGLkYqRilGKkYrRiosKEYyRipGNEYqRjBGK0YqRioqJiwmKiZGM0YoRi5GKkYrKiZGKUYqRi1GKkYrRiosKEY0RipGMEYqRjJGK0YqRioqKEYxRihGM0YoRiZGKEYqKiZGLUYoRjFGKEYqKiZGJkYoRilGKEYqKiZGM0YoRi5GKEYq evalms(pp2uu(pp)-k*pp2uu(px)): eliq:= [eliminate](%, {k,p,q});; 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 (reduce@subs)(eliq[1][1], pp); NyVJInhHNiJJInlHRiRJInpHRiQ= (reduce@subs)(eliq[2][1], pp): collect(%, px, distributed); lequi:= unapply(%,x,y,z)@OP: NyUsKioqSSJhRzYiIiIjSSJjR0YmRidJImJHRiZGJ0kieEdGJkYnISIiKiosJiomRiVGJ0YoRiciIiIqJEYoIiIlRitGL0YlRidGKkYvSSJ5R0YmRi9GKyoqLCYqJkYlRidGKUYnRi8qJEYpRjFGK0YvRiVGJ0kiekdGJkYvRipGL0YrKiosKCokRiVGMUYvRjVGK0YuRitGL0YlRidGN0YvRjJGL0YrLCoqKkYpRicsJiomRilGJ0YoRidGK0YwRi9GL0YqRi9GMkYvRi8qKkYpRicsKEY+Ri9GNUYvRjZGK0YvRjdGL0YqRi9GLyoqRiVGJ0YoRidGKUYnRjJGJ0YrKipGKUYnLCZGOkYvRjVGK0YvRjdGL0YyRi9GLywqKipGKEYnLChGLkYvRj5GL0YwRitGL0YqRi9GMkYvRi8qKkYoRicsJkY2Ri9GPkYrRi9GN0YvRipGL0YvKipGKEYnLCZGOkYvRi5GK0YvRjdGL0YyRi9GLyoqRiVGJ0Y3RidGKEYnRilGJ0Yr
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Quelles sont les coniques qui s'\303\251crivent ainsi</Font></Text-field> eq_dou-k*evalm(px &* mm &* px); {coeffs}(expand(%), px) union {condilou}; eli:= eliminate(%, {k,u,v,w,rho2}): LC4qKEkiYUc2IiIiI0kieUdGJSIiIkkiekdGJUYoRigqKEkiYkdGJUYmRilGKEkieEdGJUYoRigqKEkiY0dGJUYmRidGKEYsRihGKComSSVyaG8yR0YlRigsKEYsRihGJ0YoRilGKEYmRigqJkYxRigsKComSSJ1R0YlRihGLEYoRigqJkkidkdGJUYoRidGKEYoKiZJIndHRiVGKEYpRihGKEYoISIiKiZJImtHRiVGKCwoKiYsKComRixGKEkkbTExR0YlRihGKComRidGKEkkbTEyR0YlRihGKComRilGKEkkbTEzR0YlRihGKEYoRixGKEYoKiYsKComRixGKEZDRihGKComRidGKEkkbTIyR0YlRihGKComRilGKEkkbTIzR0YlRihGKEYoRidGKEYoKiYsKComRixGKEZFRihGKComRidGKEZMRihGKComRilGKEkkbTMzR0YlRihGKEYoRilGKEYoRihGOg== 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 collect(eli[2], [m11,m22,m33]); condicir:= subs(AAA=%, BBB= eli[1], proc(MM) zipq(mm,MM): subs(%, AAA), subs(%,BBB) end): PCQsLComSSRtMTFHNiIiIiJJImFHRiYiIiNGJyomSSJiR0YmRilJJG0yMkdGJkYnISIiKiYsJiokRihGKUYnKiRGK0YpRi1GJ0kkbTMzR0YmRidGJyomRitGKUkkbTIzR0YmRidGKSomSSRtMTNHRiZGJ0YoRikhIiMsLComLCZGMEYnKiRJImNHRiZGKUYtRidGLEYnRicqJkkkbTEyR0YmRidGKEYpRjcqJkY8RilGNEYnRilGJEYnKiZGPEYpRjJGJ0Yt (eq2mm@eqcircum)(px); tmpa,tmpb:= condicir(%): tmpa; subs(apbpc, factor(tmpb)); subs(%, pu), subs(%,rho2); (simplify@subs)(%%, eq_dou); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKWtHXzw= PCMiIiE= PCcvSSJrRzYiIiIiL0klcmhvMkdGJSokSSJSR0YlIiIjL0kidUdGJUYpL0kidkdGJUYpL0kid0dGJUYp NiQ3JSokSSJSRzYiIiIjRiRGJEYk LCgqKEkiYUc2IiIiI0kieUdGJSIiIkkiekdGJUYoRigqKEkiYkdGJUYmRilGKEkieEdGJUYoRigqKEkiY0dGJUYmRidGKEYsRihGKA== eq2mm(eqincircle); tmpa, tmpb:= condicir(%): factor(tmpa); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKT96ZD4= PCMiIiE= factor(tmpb): uu_in:= subs(%, pu): %, (factor@subs)(%%, isolate(defR2, b+a-c), rho2); NiQ3JSwkKiosKEkiYkc2IiEiIkkiY0dGKEYpSSJhR0YoIiIiRixGJ0YsRipGLCwoRitGLEYnRixGKkYsRilGKSoqLChGK0YsRipGLEYnRilGLEYrRixGKkYsRi1GKSoqLChGJ0YsRitGLEYqRilGLEYrRixGJ0YsRi1GKSwkKixGKyIiI0YnRjRGKkY0Ri0hIiNJIlJHRihGNSNGLCIiJQ== bary2norm(cent)+(bary2norm(px)-bary2norm(cent))*rad2/(rad2+eqn2): tmq:= (reduce@factor@evalmm)(%):; collect(tmq[1]/rotp(1), px, factor, distributed); invcircum:= unapply([rot3](%), x,y,z)@OP: # simplify(%%, a2toAA): collect(%, px, factor, distributed); 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 subs(ency_, tmq); funinv:= unapply(reduce(%),x,y,z)@op; 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
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Quels sont les points o\303\271 arrive un pp2uu ?</Font></Text-field> Une coordonn\303\251e \303\240 la fois evalms(pp2uu(pp)-k*pu); eli:= eliminate(%, {k,p}): nops([%]); PCUsJiomLCwqJkkiYUc2IiIiI0kicUdGKEYpIiIiKihGJ0YpRipGK0kicEdGKEYrRisqKEYtRitJImNHRihGKUYqRishIiIqJkkiYkdGKEYpRi1GKUYrKihGMkYpRipGK0YtRitGK0YrLChGLUYrRipGK0kickdGKEYrISIjRisqJkkia0dGKEYrSSJ3R0YoRitGMCwmKiYsLCooRidGKUYtRitGNUYrRisqKEYtRitGMkYpRjVGK0YwKihGL0YpRi1GK0Y1RitGKyomRi9GKUYtRilGKyomRidGKUY1RilGK0YrRjRGNkYrKiZGOEYrSSJ2R0YoRitGMCwmKiYsLCooRjVGK0YnRilGKkYrRisqKEYvRilGKkYrRjVGK0YwKihGMkYpRipGK0Y1RitGMComRjJGKUY1RilGMComRi9GKUYqRilGMEYrRjRGNkYwKiZGOEYrSSJ1R0YoRitGMA== IiIi collect(op(eli[2]), q); delta:= factor(discrim(%, q)/r^2); indets(%); conilou:= select(has,%%, a^4); 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 Ki4sKiomSSJiRzYiIiIjSSJ2R0YmIiIiISIiKiZJInVHRiZGKUYlRidGKSomSSJjR0YmRidJIndHRiZGKUYpKiZGLEYpRi5GJ0YqRicsKEYlRilJImFHRiZGKUYuRipGKSwoRjJGKUYlRilGLkYpRiksKEYyRilGLkYpRiVGKkYpLChGJUYqRi5GKkYyRilGKSwuKiZGLEYnRjIiIiVGKSoqRjJGJ0YsRilGJUYnRihGKSEiIyoqRjJGJ0YsRilGLkYnRi9GKUY6KipGJUYnRihGKUYuRidGL0YpRjoqJkYlRjhGKEYnRikqJkYuRjhGL0YnRilGKQ== PChJImFHNiJJImJHRiRJImNHRiRJInVHRiRJInZHRiRJIndHRiQ= LC4qJkkidUc2IiIiI0kiYUdGJSIiJSIiIioqRidGJkYkRilJImJHRiVGJkkidkdGJUYpISIjKipGJ0YmRiRGKUkiY0dGJUYmSSJ3R0YlRilGLSoqRitGJkYsRilGL0YmRjBGKUYtKiZGK0YoRixGJkYpKiZGL0YoRjBGJkYp inconic, perspecteur 76, centre 141 coni_in(pp)-subs(zipq(pu,px),conilou): {coeffs}(%, px); solve(%, {p,q,r}): subs(%, pp); ency(%); (reduce@barymul)(%%, complem(%%)); ency(%); PCgsJiokSSJiRzYiIiIlISIiKiRJInFHRiYhIiMiIiIsJiokSSJwR0YmRitGLCokSSJhR0YmRidGKCwmKiRJInJHRiZGK0YsKiRJImNHRiZGJ0YoLCYqJkYxIiIjRjZGOUY5KiZGL0YoRjRGKEYrLCYqJkYvRihGKkYoRisqJkYxRjlGJUY5RjksJiomRjRGKEYqRihGKyomRiVGOUY2RjlGOQ== NyUqJEkiYUc2IiEiIyokSSJiR0YlRiYqJEkiY0dGJUYm IiN3 NyUsJiokSSJiRzYiIiIjIiIiKiRJImNHRiZGJ0YoLCZGKUYoKiRJImFHRiZGJ0YoLCZGLEYoRiRGKA== IiRUIg== Les contacts de l'ellipse sont les pp2uu des sommets pp2uu(pa), pp2uu(pb), pp2uu(pc); NiU3JSIiISokSSJjRzYiIiIjKiRJImJHRidGKDclRiVGJCokSSJhR0YnRig3JUYpRixGJA== (numer@pp2uu)(px)[1]; discrim(%, y); LCwqKEkiYUc2IiIiI0kieUdGJSIiIkkiekdGJUYoISIiKihJImNHRiVGJkYnRihGKUYoRigqKEkiYkdGJUYmRidGKEYpRihGKComRi5GJkYpRiZGKComRidGJkYsRiZGKA== KiZJInpHNiIiIiMsLiomSSJiR0YkRiVJImNHRiRGJSEiIyomSSJhR0YkRiVGKEYlRioqJkYsRiVGKUYlRioqJEYsIiIlIiIiKiRGKUYvRjAqJEYoRi9GMEYw Les points \303\240 l'infini donneraient.... le centre de gravit\303\251 (reduce@pp2uu)(pp): (reduce@factor@subs)(zipq(pp, prm_inf(pdr)),%); NyUiIiJGI0Yj Il faut conilou n\303\251gatif pour que q soit r\303\251el solq:= factor([solve](op(eli[2]), {q})): subs(apbpc, conilou=-con^2, solq): solqq:= simplify(%) assuming a>0,b>0,c>0,R>0, con>0, -b^2*v+u*b^2+c^2*w-u*c^2 >0: Test de conjugaison factor(subs(solqq[1],q/r)+subs(solqq[2],q/r)): indets(%); PChJImFHNiJJImJHRiRJImNHRiRJInVHRiRJInZHRiRJIndHRiQ= defR2; LyokSSJSRzYiIiIjLCQqMEkiYUdGJUYmSSJiR0YlRiZJImNHRiVGJiwoRioiIiJGKUYtRishIiJGLiwoRilGLUYqRi1GK0YtRi4sKEYpRi1GK0YtRipGLkYuLChGKkYuRitGLkYpRi1GLkYu (factor@subs)(eli[1], solqq[1], pp): (factor@subs)(con^2=-conilou, collect(%, con)): tmp:= (expand@reduce)(%): (reduce@factor@subs)(con^2=-conilou, defR2, tmp): tmp1:= collect(%, con, factor): collect(add(k, k=tmp1), con, factor): tmp2:= expand(evalmm(subs(con=-con, %)*tmp1)): tmp3:= (reduce@factor@subs)(con^2=-conilou, defR2, tmp2): Et on a enfin une \303\251quation sym\303\251trique tmp4:= collect(tmp3, [con,R], U-> collect(U, pu, factor, distributed)); factor(rot(tmp4[1])/tmp4[2]); 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 IiIi subs(con=0, tmp4); part1:= Vector(map(U-> a*b*c*map(V->V/a/b/c,U),%)); 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 LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpbyo+ayU= part2:= (Vector@map2)(select,has,tmp4,R); LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIoXyh6ZA==
<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">Le graphe des points dont un multiple v\303\251rifie condilou</Font></Text-field> Pour un point u:v:w, il n'est pas toujours possible de trouver un k qui aille bien. condi1:= subs(u=k*u,v=k*v,w=k*w, condilou): factor(discrim(%, k)); IiIh subs(zipq(pu, pX(8)), ency_, condi1); solve(%); LCQqKCIpU3dgIyoiIiIpSSJxRzYiIiIjRiUpSSJrR0YoRilGJUYl NiY8JC9JImtHNiJGJS9JInFHRiYiIiFGIzwkL0YlRikvRihGKEYq (factor@subs)(ency_, cetriangle, bary2proj(pp2uu(pp))): funlou:= unapply(subsop(3=NULL, %),p,q,r)@op; LUkiQEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkZio2JUkicEdGJ0kicUdGJ0kickdGJ0YnNiRJKW9wZXJhdG9yR0YnSSZhcnJvd0dGJ0YnNyQsJComLC4qJjklIiIiOSZGNyEpOV1PRSokRjgiIiMhKFAvZygqJEY2RjshKSZHISo+IyomRjhGNzkkRjciKCd6JD4pKiRGQEY7IighUk8mKSomRjZGN0ZARjciKDchKm8iRjcsLkY1IiQ5I0Y6IiQ8IkY9IiQwI0Y/IiRDIkZCIiRdI0ZEISNfISIiI0ZNIicsSzcsJCooIiNOI0Y3RjssLEY/IiYyIm9GQiInck85RjoiJnQoPkY9IiYqZkFGRCEmVkUkRjdGRkZNIyEjS0ZPRidGJ0YnSSNvcEdGJQ== (expand@subs)(zipq(pu, projx), ency_, conilou):evalf(%/10000); pl1:= implicitplot(%, X=-0.4..1, Y=-1..0, grid=[50,50], thickness=3): LC5JIlhHNiIkIStycDdfOCEiKSokRiMiIiMkIisrJmYqM2whIipJIllHRiQkIitXMms9QEYnKiRGLUYpJCIrTHpdVjpGJyomRi0iIiJGI0Y0JCEra0o/Rj5GJyQiKzktIj45KEYsRjQ= pl2:= pointplot([seq](funlou(xyz[j]), j=1..jmax)): pl20:= pointplot([seq](`if`(ff[j]=1,funlou(xyz[j]),NULL), j=1..jmax)): [color=blue]: pl0:= dralinpts(pa,pb,%),dralinpts(pb,pc,%),dralinpts(pc,pa,%): pl3:= drawna(pX(141),"c",2,[color=blue]): Magnifique accord des deux graphes display(pl0, pl1, pl3, pl20, view=[-1.5..1.5,-1.5..0.5], scaling=constrained); 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ckoi:= (reduce@factor@subs)(eli[1][1], pp): map(length, %); NyUiJFwjIiQsIkYk ckoi2:= simplify(ckoi, {condilou}):map(length, %); NyUiJFwjIiREIkYk
<Text-field style="Heading 1" layout="Heading 1">Vrac</Text-field> incircle= conicev(X7,X7) pX(7); zipd(cyclocev(%), %); conicev(pX(7), pX(7)); eq2mm(%); 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 LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUYjNiYtSSVtcm93R0YkNiotSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRjQvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRidGMEY3RjAvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUpcmVhZG9ubHlHRj1GNEY0LyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRjRGVkZZ 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 LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKXMjSFci nine_points_circle=conicev(X2, X4) zipq(pp,pX(2)),zipq(pu, normal(cyclocev(pX(2))/2)): tmp:= conicev(pX(2),pX(4)); eq2mm(%); LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEkdG1wRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GIzYuLUYjNiYtSSVtc3VwR0YkNiUtRiw2JVEieEYnRi9GMi1JI21uR0YkNiRRIjJGJ0Y5LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1GNjYtUTEmSW52aXNpYmxlVGltZXM7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZORl5vLUkobWZlbmNlZEdGJDYkLUYjNigtRiM2JC1GVDYlLUYsNiVRImJGJ0YvRjJGWUZnbkY5LUY2Ni1RIitGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GYHAtRiM2JC1GVDYlLUYsNiVRImNGJ0YvRjJGWUZnbkY5LUY2Ni1RKCZtaW51cztGJ0Y5RjtGPkZARkJGREZGRkhGX3BGYXAtRiM2JC1GVDYlLUYsNiVRImFGJ0YvRjJGWUZnbkY5RjlGOUY5RmlwLUYjNipGWUZqbkZnb0Zqbi1GLDYlUSJ6RidGL0YyRmpuRlZGOUZpcC1GIzYqRllGam5GVkZqbi1GLDYlUSJ5RidGL0YyRmpuRmRwRjlGXHAtRiM2Ji1GVDYlRmpxRllGZ25Gam4tRmFvNiQtRiM2KEZicEZccEZccUZpcEZlb0Y5RjlGOUZpcC1GIzYqRllGam5GZXFGam5GanFGam5GXnFGOUZccC1GIzYmLUZUNiVGZXFGWUZnbkZqbi1GYW82JC1GIzYoRlxxRlxwRmVvRmlwRmJwRjlGOUY5RjkvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUpcmVhZG9ubHlHRj1GOQ== LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKXMnSFAm
<Text-field style="Heading 1" layout="Heading 1">Cercles en tout genre (il faut Digits = 30)</Text-field> Digits:=30: Le kit circle # valr := r = (1/2)*a*b*c/((a+b+c)*R) # kitcircle:= isolate(defR, S), vale, valom, valr, s=(a+b+c)/2; kitcircle := S = (1/4)*a*b*c/R, e = sqrt(-a^2*c^2+c^4-b^2*c^2-a^2*b^2+a^4+b^4)/sqrt(a^2*b^2+a^2*c^2+b^2*c^2), {cos(omega) = (1/2)*(a^2+b^2+c^2)/sqrt(a^2*b^2+a^2*c^2+b^2*c^2), sin(omega) = (1/2)*a*b*c/(R*sqrt(a^2*b^2+a^2*c^2+b^2*c^2))}, s = (1/2)*a+(1/2)*b+(1/2)*c, r = (1/2)*a*b*c/((a+b+c)*R); 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 WW1:= sqrt(a^2*b^2+a^2*c^2+b^2*c^2); WW2:= sqrt(-a^2*c^2+c^4-b^2*c^2-a^2*b^2+a^4+b^4); WW3:= sqrt(a^6-a^4*b^2-a^4*c^2-a^2*b^4+3*a^2*b^2*c^2-a^2*c^4+b^6-b^4*c^2-b^2*c^4+c^6); WW4:= sqrt(b^3-b^2*c-b*c^2+c^3-a*b^2+3*a*b*c-a*c^2-a^2*b-a^2*c+a^3); KiQpLCgqJilJImFHNiIiIiMiIiIpSSJiR0YoRilGKkYqKiZGJkYqKUkiY0dGKEYpRipGKiomRitGKkYuRipGKiNGKkYpRio= KiQpLC4qJilJImFHNiIiIiMiIiIpSSJjR0YoRilGKiEiIiokKUYsIiIlRipGKiomKUkiYkdGKEYpRipGK0YqRi0qJkYmRipGMkYqRi0qJClGJ0YwRipGKiokKUYzRjBGKkYqI0YqRilGKg== KiQpLDYqJClJImFHNiIiIiciIiJGKiomKUkiYkdGKCIiI0YqKUYnIiIlRiohIiIqJilJImNHRihGLkYqRi9GKkYxKiYpRi1GMEYqKUYnRi5GKkYxKioiIiRGKkY3RipGLEYqRjNGKkYqKiYpRjRGMEYqRjdGKkYxKiQpRi1GKUYqRioqJkY2RipGM0YqRjEqJkYsRipGO0YqRjEqJClGNEYpRipGKiNGKkYuRio= KiQpLDYqJClJImFHNiIiIiQiIiJGKiomSSJjR0YoRiopRiciIiNGKiEiIiomSSJiR0YoRipGLUYqRi8qJkYnRiopRjFGLkYqRi8qKkYpRipGJ0YqRjFGKkYsRipGKiomRidGKilGLEYuRipGLyomRixGKkYzRipGLyokKUYxRilGKkYqKiQpRixGKUYqRioqJkYxRipGNkYqRi8jRipGLkYq pytha(pp,px): factor(%): collect(%, px, U->collect(U, pp, factor, distributed), distributed): subs(a2toAA,%); 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
map(1/id, defR2)*a^2*b^2*c^2: ruleR:= -(expand@(rhs=lhs))(%); LywuKiZJImFHNiIiIiNJImJHRiZGJyEiIyomRiVGJ0kiY0dGJkYnRikqJkYoRidGK0YnRikqJEYrIiIlIiIiKiRGJUYuRi8qJEYoRi5GLywkKipGJUYnRihGJ0YrRidJIlJHRiZGKSEiIg== Antipodes sur le circumcircle _P:= pp; _O1:=pX(3); _PP:= collect(reflection(_O1,pp), pp, factor); NyVJInBHNiJJInFHRiRJInJHRiQ= NyUqJkkiYUc2IiIiIywoKiRGJEYmISIiKiRJImJHRiVGJiIiIiokSSJjR0YlRiZGLEYsKiZGK0YmLChGLUYsRihGLEYqRilGLComRi5GJiwoRihGLEYqRixGLUYpRiw= NyUsKCooLCgqJEkiY0c2IiIiIyIiIiokSSJhR0YoRilGKiokSSJiR0YoRikhIiJGKiwoRitGKkYtRipGJkYvRipJInBHRihGKkYvKihGLEYpLChGK0YqRi1GL0YmRi9GKkkicUdGKEYqISIjKihGLEYpRjNGKkkickdGKEYqRjUsKCooRi5GKUYlRipGMUYqRikqKEYwRipGM0YqRjRGKkYqKihGLkYpRiVGKkY3RipGKSwoKihGJ0YpRjBGKkYxRipGKSooRidGKUYwRipGNEYqRikqKEYlRipGM0YqRjdGKkYq _P1:= prm_cir(pdr); _PP1:= (elimifacu@reflection)(_O1,%): collect(%, pdr): Vector(%);;; NyUqJkkiYUc2IiIiIywmSSZzaWdtYUdGJSIiIkkkdGF1R0YlISIiRisqJkkiYkdGJUYmLCZJJHJob0dGJUYrRipGKUYrKiZJImNHRiVGJiwmRi9GKUYoRitGKw== LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIoP241Jw==
<Text-field style="Heading 1" layout="Heading 1">Circumcircle </Text-field> num_cent:=3; cent:= pX(%): rad2:= (R)^2; IiIk KiRJIlJHNiIiIiM= (factor@pp2uu)(cent): ccir_uu:= (Vector@factor@subs)(apbpc,%); ici_uu:=%: ency(%); LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIoP2hXJg== IiIj subs(rho2=rad2, zipq(Vector(pu), ici_uu), eq_dou): (factor@subs)(defR2, %); eqn0:= sort(collect(%, px, factor, distributed), [x,y,z]); LCgqKEkiY0c2IiIiI0kieEdGJSIiIkkieUdGJUYoRigqKEkiYkdGJUYmRidGKEkiekdGJUYoRigqKEkiYUdGJUYmRilGKEYsRihGKA== LCgqKEkiY0c2IiIiI0kieEdGJSIiIkkieUdGJUYoRigqKEkiYkdGJUYmRidGKEkiekdGJUYoRigqKEkiYUdGJUYmRilGKEYsRihGKA== circlefunction:= subs(y=0,z=0,x=1,eqn0)/b/c; fac:=1: ici_eqn:= Sum(coeff(eqn0,x,2)*x^2,j)+fac*Sum(coeff(coeff(eqn0,y),z)/fac*y*z,j); LCYtSSRTdW1HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCIiIUkiakdGKCIiIi1GJDYkKihJImFHRigiIiNJInlHRihGLEkiekdGKEYsRitGLA== (factor@mm2persp@eq2mm)(eqn0): ici_persp:= elimifacu(%); ency(%); NyUqJEkiYUc2IiIiIyokSSJiR0YlRiYqJEkiY0dGJUYm IiIn rad2-eqn0/(x+y+z)^2; LCYqJEkiUkc2IiIiIyIiIiomLCgqKEkiY0dGJUYmSSJ4R0YlRidJInlHRiVGJ0YnKihJImJHRiVGJkYsRidJInpHRiVGJ0YnKihJImFHRiVGJkYtRidGMEYnRidGJywoRixGJ0YtRidGMEYnISIjISIi tmp:= bary2norm(cent)+(bary2norm(px)-bary2norm(cent))*rad2/(rad2-eqn0/(x+y+z)^2): tmq:= (reduce@factor@evalmm)(%): (Vector@factor@subs)(defR2, %): collect(-%/rotp(a^2), px, normal@expand, distributed); LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpdyIqUnE= les fonctions funon, funinv, funsym (reduce@factor@evalmm@subs)(ency_, tmp): funinv:= unapply(%,x,y,z)@op: funon:= unapply(subs(ency_, eqn0), x,y,z)@op: (reduce@subs)(ency_, reflection(pX(3),px)): funsym:= unapply(%,x,y,z)@op: Bien r\303\251gler le seuil... ou bien passer \303\240 20 chiffres ici_on:= [seq](`if`((abs@funon)(xyz[j])<Float(1,-6),j,NULL),j=1..jmax): nops(%); IiRlIw== Points \303\240 l'infini sans isogon nomm\303\251 seq(`if`(ff[j]=1 and gg[j]=0,j,NULL), j=1..jmax); nops([%]); 12,19,36,58,101; seq(ency( (bary2norm)(pX(j))-bary2norm(pX(2))), j=%); NisiJEgmIiRNJiIkTiYiJFMmIiRXJiIkKSkpIiU3PiIlUT4iJVk+ IiIq NiciIzciIz4iI08iI2UiJCwi NiciJEgmIiRNJiIkTiYiJFMmIiRXJg== Les antipodaux qqr:= table(): for j in ici_on do tmp:= ency(funsym(xyz[j])): if tmp <>`?` then qqr[j]:= tmp; fi; od: j:='j': lesk:= sort(map(op,[indices](qqr))); nops(%); bad_points=seq(`if`(qqr[qqr[j]]=j,NULL,j), j=lesk); 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 IiRDIg== L0krYmFkX3BvaW50c0c2IkYk Il faut envoyer cela ***si besoin*** dans un r\303\251pertoire lisible et navigable if false then try close(fd); catch : end try; fd := open("/home/douillet/public_html/etc/alt_data.csv", WRITE): for j in lesk do fprintf(fd, """%d"";""%d""\134n", j, qqr[j]); od: close(fd); j:='j': fi:
<Text-field style="Heading 1" layout="Heading 1">Incircle + antipodie</Text-field> num_cent:=1; cent:= pX(%): rad2:= (subs(kitcircle, r))^2; IiIi LCQqLEkiYUc2IiIiI0kiYkdGJUYmSSJjR0YlRiYsKEYkIiIiRidGKkYoRiohIiNJIlJHRiVGKyNGKiIiJQ== in_rad:= map(sqrt, rad2) assuming a>0,b>0,c>0,R>0; ici_rad:= %: LCQqLEkiY0c2IiIiIkkiYkdGJUYmSSJhR0YlRiYsKEYoRiZGJ0YmRiRGJiEiIkkiUkdGJUYqI0YmIiIj (factor@pp2uu)(cent): in_uu:= (Vector@factor@subs)(defR2,%); ici_uu:=%: ency(%); LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpJzQnUl0= IiQ3JA== subs(rho2=rad2, valR22, zipq(Vector(pu), ici_uu), eq_dou): eqn0:= sort(collect(%, px, factor, distributed), [x,y,z]); LC4qJiwoSSJiRzYiISIiSSJjR0YmRidJImFHRiYiIiIiIiNJInhHRiZGKyNGJyIiJSoqRiRGKiwoRilGKkYoRipGJUYnRipGLEYqSSJ5R0YmRiojRidGKyoqRiRGKiwoRiVGKkYpRipGKEYnRipGLEYqSSJ6R0YmRipGMiomRjBGK0YxRitGLSoqRjBGKkY0RipGMUYqRjVGKiNGKkYrKiZGNEYrRjVGK0Yt circlefunction:= subs(y=0,z=0,x=1,eqn0)/b/c; LCQqKCwoSSJiRzYiISIiSSJjR0YmRidJImFHRiYiIiIiIiNGJUYnRihGJyNGJyIiJQ==
<Text-field style="Heading 2" layout="Heading 2">antipodie</Text-field> _O1:= pX(3); _O2:= cent; NyUqJkkiYUc2IiIiIywoKiRGJEYmISIiKiRJImJHRiVGJiIiIiokSSJjR0YlRiZGLEYsKiZGK0YmLChGLUYsRihGLEYqRilGLComRi5GJiwoRihGLEYqRixGLUYpRiw= NyVJImFHNiJJImJHRiRJImNHRiQ= (R*bary2norm(cent)- ici_rad*bary2norm(pX(3)))/(R-ici_rad): (reduce@FActor@evalmm)(%): _V:= (elimifacu@FActor@subs)(defR2, %); ency(%); NyUqJkkiYUc2IiIiIywoSSJiR0YlISIiSSJjR0YlRilGJCIiIkYpLCQqJkYoRiYsKEYkRitGKkYrRihGKUYpRiksJComRipGJiwoRihGK0YkRitGKkYpRilGKQ== IiNj (R*bary2norm(cent) + ici_rad*bary2norm(pX(3)))/(R+ici_rad): (reduce@FActor@evalmm)(%): _U:= (elimifacu@FActor@subs)(defR2, %);ency(%); NyUqJkkiYUc2IiIiIywoSSJiR0YlISIiSSJjR0YlRilGJCIiIkYrLCQqJkYoRiYsKEYkRitGKkYrRihGKUYrRiksJComRipGJiwoRihGK0YkRitGKkYpRitGKQ== IiNi (reduce@factor@wedge)(wedge(_P,_U),wedge(_PP,_V)): collect(%, pp, factor): _Q:= Vector(xcollect(%, [rot3](-a+b+c))); LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpcyVwKlI= (elimifacu@factor@wedge)(wedge(_PP,_U),wedge(_P,_V)): collect(%, pp, factor): _QQ:= Vector(xcollect(-%, [rot3](-a+b+c))); (reduce@factor)(bary2norm(_Q)+bary2norm(_QQ))=cent; LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpR1BLUw== LzclSSJhRzYiSSJiR0YlSSJjR0YlRiM= fac:=a^2: subs(zipq(pp, prm_cir(pdr)), _Q): %[1]: map(U-> U/fac, op(1,%))*fac*op(2,%): _Qprm:= Vector([rot3](%)); LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpUzk1Xg== fac:=a^2: subs(zipq(pp, prm_cir(pdr)), _QQ): %[1]: map(U-> U/fac, op(1,%))*fac*op(2,%): _QQprm:= Vector([rot3](%)); LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpTyRlZiU= unapply(eqn0, x,y,z)@OP: map(factor@%, [_Q,_QQ,_Qprm,_QQprm]): subs(eqcircum(pp)=0, %);; NyYiIiFGI0YjRiM=
facxx, facyz:=-1/4, 1/2: ici_eqn:= facxx*Sum(coeff(eqn0,x,2)/facxx*x^2,j)+ facyz*Sum(coeff(coeff(eqn0,y),z)/facyz*y*z,j); LCYtSSRTdW1HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JComLChJImJHRighIiJJImNHRihGLUkiYUdGKCIiIiIiI0kieEdGKEYxIiU6TiNGLSIiJS1GJDYkKiosKEYvRjBGLkYwRixGLUYwLChGLEYwRi9GMEYuRi1GMEkieUdGKEYwSSJ6R0YoRjBGMyNGMEYx (factor@mm2persp@eq2mm)(eqn0): ici_persp:= elimifacu(%); ency(%); NyUqJCwoSSJiRzYiISIiSSJjR0YmRidJImFHRiYiIiJGJywkKiQsKEYpRipGKEYqRiVGJ0YnRicsJCokLChGJUYqRilGKkYoRidGJ0Yn IiIo tmp_inv:= bary2norm(cent)+(bary2norm(px)-bary2norm(cent))*rad2/(rad2-eqn0/(x+y+z)^2): tmq:= (reduce@factor@evalmm)(%): (Vector@factor@subs)(defR2, %): collect(-%/rotp(a^2), px, normal@expand, distributed); LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpS1EiPig= les fonctions funon, funinv, funsym (reduce@factor@evalmm@subs)(ency_, tmp_inv): funinv:= unapply(%,x,y,z)@op: funon:= unapply(subs(ency_, eqn0), x,y,z)@op: (reduce@subs)(ency_, reflection(cent,px)): funsym:= unapply(%,x,y,z)@op: Bien r\303\251gler le seuil... ou bien passer \303\240 20 chiffres ici_on:= [seq](`if`((abs@funon)(xyz[j])<Float(1,-6),j,NULL),j=1..jmax): nops(%); IiNS Les inverses-in-circle qqr:= table(): for j to jmax do if ff[j]=1 then next fi; tmp:= ency(funinv(xyz[j])): if tmp <>`?` then qqr[j]:= tmp; fi; od: # j:='j': ici_inv:= sort(map(op,[indices](qqr))); nops(%); bad_points=seq(`if`(qqr[qqr[j]]=j,NULL,j), j=ici_inv); N1ciIigiIzYiI08iI2wiIyEpIiRhJCIkVSoiJFkqIiViNiIlOTgiJTo4IiU8OCIlPjgiJUI4IiVhOCIlYjgiJWM4IiVkOCIlZTgiJWY4IiVnOCIlaDgiJWk4IiVqOCIlazgiJWw4IiVtOCIlbjgiJShRIiIlJnkiIiVZQyIlWkMiJUBJIiVBSSIlQkkiJUNJIiVESSIlRUkiJUZJIiVHSSIlPUwiJT5MIiU/TCIlQEwiJUFMIiVCTCIlQ0wiJURMIiVFTCIlRkwiJUdMIiU4TiIlOU4= IiNg L0krYmFkX3BvaW50c0c2IkYk On doit retrouver le nombre de points sur le cercle [seq](`if`(qqr[j]=j,j,NULL),j=ici_inv): nops(%); IiNS Les antipodaux qqr:= table(): for j in ici_on do tmp:= ency(funsym(xyz[j])): if tmp <>`?` then qqr[j]:= tmp; fi; od: j:='j': lesk:= sort(map(op,[indices](qqr))); nops(%); bad_points=seq(`if`(qqr[qqr[j]]=j,NULL,j), j=lesk); NzYiIzYiJTw4IiVlOCIlZjgiJWg4IiVpOCIlazgiJVlDIiVaQyIlQEkiJUFJIiVCSSIlQ0kiJUZJIiVHSSIlPUwiJT5MIiVBTCIlRUwiJUdM IiM/ L0krYmFkX3BvaW50c0c2IkYk Il faut envoyer cela ***si besoin*** dans un r\303\251pertoire lisible et navigable if false then try close(fd); catch : end try; fd := open("/home/douillet/public_html/etc/alt_data.csv", WRITE): for j in lesk do fprintf(fd, """%d"";""%d""\134n", j, qqr[j]); od: close(fd); j:='j': fi:
<Text-field style="Heading 1" layout="Heading 1">Nine points (new)</Text-field> num_cent:=5; cent:= pX(%): rad2:= (R/2)^2; IiIm LCQqJEkiUkc2IiIiIyMiIiIiIiU= (factor@pp2uu)(cent): in_uu:= (Vector@factor@subs)(defR2,%); ici_uu:=%: ency(%); LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpP2RoWQ== SSI/RzYi Essai pour plubo # subs(apbpc, in_uu); (factor)(add(k,k=in_uu)); in_uu-%*Vector([1,1,1]): FActor(%); subs(rho2=rad2, valR22, zipq(Vector(pu), ici_uu), eq_dou): eqn0:= sort(collect(%, px, factor, distributed), [x,y,z]); LC4qJiwoKiRJImJHNiIiIiMjISIiIiIlKiRJImNHRidGKEYpKiRJImFHRidGKCMiIiJGK0YxSSJ4R0YnRihGMSooRi1GKEYyRjFJInlHRidGMSNGMUYoKihGJkYoRjJGMUkiekdGJ0YxRjUqJiwoRixGKUYuRilGJUYwRjFGNEYoRjEqKEYvRihGNEYxRjdGMUY1KiYsKEYuRilGJUYpRixGMEYxRjdGKEYx circlefunction:= subs(y=0,z=0,x=1,eqn0)/b/c; facxx, facyz:=-1/4, 1/2: j:='j': ici_eqn:= facxx*Sum( simplify(coeff(eqn0,x,2)/facxx)*x^2,j)+ facyz*Sum(coeff(coeff(eqn0,y),z)/facyz*y*z,j); LCYtSSRTdW1HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JComLCgqJEkiYkdGKCIiIyIiIiokSSJjR0YoRi5GLyokSSJhR0YoRi4hIiJGL0kieEdGKEYuSSJqR0YoI0Y0IiIlLUYkNiQqKEYzRi5JInlHRihGL0kiekdGKEYvRjYjRi9GLg== (factor@mm2persp@eq2mm)(eqn0): ici_persp:= elimifacu(%); ency(%); NyUqJCwqKiRJImFHNiIiIiUiIiIqJkYmIiIjSSJiR0YnRishIiIqJkYmRitJImNHRidGK0YtKiZGLEYrRi9GK0YtRi0sJCokLCpGMEYpRipGKSokRixGKEYtRi5GKUYtRi0sJCokLCpGLkYpRjBGKSokRi9GKEYtRipGKUYtRi0= SSI/RzYi tmp_inv:= bary2norm(cent)+(bary2norm(px)-bary2norm(cent))*rad2/(rad2-eqn0/(x+y+z)^2): #tmq:= (reduce@factor@evalmm)(%): (Vector@factor@subs)(defR2, %): #collect(-%/rotp(a^2), px, normal@expand, distributed); les fonctions funon, funinv, funsym (reduce@factor@evalmm@subs)(ency_, tmp_inv): funinv:= unapply(%,x,y,z)@op: funon:= unapply(subs(ency_, eqn0), x,y,z)@op: (reduce@subs)(ency_, reflection(cent,px)): funsym:= unapply(%,x,y,z)@op: Bien r\303\251gler le seuil... ou bien passer \303\240 20 chiffres ici_on:= [seq](`if`((abs@funon)(xyz[j])<Float(1,-6),j,NULL),j=1..jmax): nops(%); IiNQ Les inverses-in-circle qqr:= table(): for j to jmax do if ff[j]=1 then next fi; tmp:= ency(funinv(xyz[j])): if tmp <>`?` then qqr[j]:= tmp; fi; od: # j:='j': ici_inv:= sort(map(op,[indices](qqr))); nops(%); bad_points=seq(`if`(qqr[qqr[j]]=j,NULL,j), j=ici_inv); N1kiIiMiIiQiIiUiIzYiJDgiIiQ5IiIkOiIiJDsiIiQ8IiIkPSIiJD4iIiQ/IiIkQCIiJEEiIiRCIiIkQyIiJEQiIiRFIiIkRiIiJEciIiRIIiIkSSIiJEoiIiRLIiIkTCIiJE0iIiROIiIkTyIiJFAiIiRRIiIkUiIiJFQiIiQnPSIkLiUiJEYlIiRvJSIkQiciJEMnIiREJyIkZSkiJTc4IiU4OCIlOzgiJWc6IiVtOiIlJWYiIiVSPyIlUz8iJXM/IiVdQyIlekUiJU1KIiVhSiIlZUsiJWZL IiNi L0krYmFkX3BvaW50c0c2IkYk On doit retrouver le nombre de points sur le cercle [seq](`if`(qqr[j]=j,j,NULL),j=ici_inv): nops(%); IiNQ Les antipodaux qqr:= table(): for j in ici_on do tmp:= ency(funsym(xyz[j])): if tmp <>`?` then qqr[j]:= tmp; fi; od: j:='j': lesk:= sort(map(op,[indices](qqr))); nops(%); bad_points=seq(`if`(qqr[qqr[j]]=j,NULL,j), j=lesk); NzoiIzYiJDgiIiQ5IiIkOiIiJDsiIiQ8IiIkPSIiJD4iIiRBIiIkQyIiJEQiIiRGIiIkRyIiJEgiIiRJIiIkSiIiJEsiIiRMIiIkTyIiJFAiIiU3OCIlODgiJVI/IiVTPw== IiND L0krYmFkX3BvaW50c0c2IkYk Il faut envoyer cela ***si besoin*** dans un r\303\251pertoire lisible et navigable if false then try close(fd); catch : end try; fd := open("/home/douillet/public_html/etc/alt_data.csv", WRITE): for j in lesk do fprintf(fd, """%d"";""%d""\134n", j, qqr[j]); od: close(fd); j:='j': fi:
<Text-field style="Heading 1" layout="Heading 1">Bevan : circumcircle of excentral triangle (new)</Text-field> num_cent:=40; cent:= pX(%): rad2:= (2*R)^2; IiNT LCQqJEkiUkc2IiIiIyIiJQ== (factor@pp2uu)(cent): bev_uu:= (Vector@factor@subs)(defR2,%); ici_uu:=%: ency(%); LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpN2hTYA== SSI/RzYi map(normal@simplify, bev_uu, {ruleR}): bev_uu:= (EXpand@subs)(isolate(ruleR, a^4), %); LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpM2lAcw== subs(rho2=rad2, valR22, zipq(Vector(pu), ici_uu), eq_dou): eqn0:= sort(collect(%, px, factor, distributed), [x,y,z]); LC4qKEkiYkc2IiIiIkkiY0dGJUYmSSJ4R0YlIiIjRiYqKkYnRiYsKEkiYUdGJUYmRiRGJkYnRiZGJkYoRiZJInlHRiVGJkYmKipGJEYmRitGJkYoRiZJInpHRiVGJkYmKihGLEYmRidGJkYtRilGJioqRixGJkYrRiZGLUYmRi9GJkYmKihGLEYmRiRGJkYvRilGJg== circlefunction:= subs(y=0,z=0,x=1,eqn0)/b/c; facxx, facyz:=1, a+b+c: j:='j': ici_eqn:= facxx*Sum( simplify(coeff(eqn0,x,2)/facxx)*x^2,j)+ facyz*Sum(coeff(coeff(eqn0,y),z)/facyz*y*z,j); LCYtSSRTdW1HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCooSSJiR0YoIiIiSSJjR0YoRixJInhHRigiIiNJImpHRihGLComLChJImFHRihGLEYrRixGLUYsRiwtRiQ2JCooRjNGLEkieUdGKEYsSSJ6R0YoRixGMEYsRiw= (factor@mm2persp@eq2mm)(eqn0): ici_persp:= elimifacu(%); ency(%); NyUqJkkiYUc2IiIiIiwoSSJiR0YlISIiSSJjR0YlRilGJEYmRiksJComRihGJiwoRiRGJkYqRiZGKEYpRilGKSwkKiZGKkYmLChGKEYmRiRGJkYqRilGKUYp IiNk tmp_inv:= bary2norm(cent)+(bary2norm(px)-bary2norm(cent))*rad2/(rad2-eqn0/(x+y+z)^2): #tmq:= (reduce@factor@evalmm)(%): (Vector@factor@subs)(defR2, %): #collect(-%/rotp(a^2), px, normal@expand, distributed); les fonctions funon, funinv, funsym (reduce@factor@evalmm@subs)(ency_, tmp_inv): funinv:= unapply(%,x,y,z)@op: funon:= unapply(subs(ency_, eqn0), x,y,z)@op: (reduce@subs)(ency_, reflection(cent,px)): funsym:= unapply(%,x,y,z)@op: Bien r\303\251gler le seuil... ou bien passer \303\240 20 chiffres Digits:=20: ici_on:= [seq](`if`((abs@funon)(xyz[j])<Float(1,-6),j,NULL),j=1..jmax): nops(%); IiIq Les inverses-in-circle qqr:= table(): for j to jmax do if ff[j]=1 then next fi; tmp:= ency(funinv(xyz[j])): if tmp <>`?` then qqr[j]:= tmp; fi; od: # j:='j': ici_inv:= sort(map(op,[indices](qqr))); nops(%); bad_points=seq(`if`(qqr[qqr[j]]=j,NULL,j), j=ici_inv); NzUiIiIiI08iI1kiI2QiJCVbIiVZNSIlYTUiJWI2IiV3NyIleDciJSNHIiIlbzwiJStAIiUsQCIlW0MiJVxDIiVbSCIlZkgiJWtN IiM+ L0krYmFkX3BvaW50c0c2IkYk On doit retrouver le nombre de points sur le cercle [seq](`if`(qqr[j]=j,j,NULL),j=ici_inv): nops(%); IiIq Les antipodaux qqr:= table(): for j in ici_on do tmp:= ency(funsym(xyz[j])): if tmp <>`?` then qqr[j]:= tmp; fi; od: j:='j': lesk:= sort(map(op,[indices](qqr))); nops(%); bad_points=seq(`if`(qqr[qqr[j]]=j,NULL,j), j=lesk); NyYiJStAIiUsQCIlW0MiJVxD IiIl L0krYmFkX3BvaW50c0c2IkYk Digits:=10: Il faut envoyer cela ***si besoin*** dans un r\303\251pertoire lisible et navigable if false then try close(fd); catch : end try; fd := open("/home/douillet/public_html/etc/alt_data.csv", WRITE): for j in lesk do fprintf(fd, """%d"";""%d""\134n", j, qqr[j]); od: close(fd); j:='j': fi:
<Text-field style="Heading 1" layout="Heading 1">Brocard (new)</Text-field> num_cent:=182; cent:= pX(%); IiQjPQ== NyUqJkkiYUc2IiIiIywoKiRGJCIiJSIiIiomRiRGJiwmKiRJImJHRiVGJkYqKiRJImNHRiVGJkYqRiohIiIqJkYuRiZGMEYmISIjRioqJkYuRiYsKCokRi5GKUYqKiZGLkYmLCZGL0YqKiRGJEYmRipGKkYxKiZGJEYmRjBGJkYzRioqJkYwRiYsKCokRjBGKUYqKiZGMEYmLCZGOUYqRi1GKkYqRjEqJkYkRiZGLkYmRjNGKg== rad2:= subs(kitcircle, defR2, (e*R/cos(omega)/2)^2 ); LCQqNCwuKiZJImFHNiIiIiNJImNHRidGKCEiIiokRikiIiUiIiIqJkkiYkdGJ0YoRilGKEYqKiZGJkYoRi9GKEYqKiRGJkYsRi0qJEYvRixGLUYtRiZGKEYvRihGKUYoLChGL0YtRiZGLUYpRipGKiwoRiZGLUYvRi1GKUYtRiosKEYmRi1GKUYtRi9GKkYqLChGL0YqRilGKkYmRi1GKiwoKiRGJkYoRi0qJEYvRihGLSokRilGKEYtISIjRio= (factor@pp2uu)(cent): broc_uu:= (Vector@factor@subs)(defR2,%); ici_uu:=%: ency(%); LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpWys4Uw== SSI/RzYi broc_uu:= map(sort, subs(apbpc, broc_uu), [a,b,c]); LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpO2U3Og== subs(rho2=rad2, valR22, zipq(Vector(pu), ici_uu), eq_dou): eqn0:= sort(collect(%, px, factor, distributed), [x,y,z]); LC4qKkkiYkc2IiIiI0kiY0dGJUYmLCgqJEkiYUdGJUYmIiIiKiRGJEYmRisqJEYnRiZGKyEiIkkieEdGJUYmRi4qKkYnIiIlRihGLkYvRitJInlHRiVGK0YrKipGJEYxRihGLkYvRitJInpHRiVGK0YrKipGKkYmRidGJkYoRi5GMkYmRi4qKkYqRjFGKEYuRjJGK0Y0RitGKyoqRipGJkYkRiZGKEYuRjRGJkYu circlefunction:= subs(y=0,z=0,x=1,eqn0)/b/c; facxx, facyz:=1/(a^2+b^2+c^2) $2: j:='j': A(facxx)*Sum( simplify(coeff(eqn0,x,2)/facxx)*x^2,j)+ A(facyz)*Sum(coeff(coeff(eqn0,y),z)/facyz*y*z,j): ici_eqn:= sort(%, [x,y,z]); LCYqJi1JIkFHNiI2IyokLCgqJEkiYUdGJiIiIyIiIiokSSJiR0YmRixGLSokSSJjR0YmRixGLSEiIkYtLUkkU3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiQsJCooRjFGLEYvRixJInhHRiZGLEYySSJqR0YmRi1GLSomRiRGLS1GNDYkKihGKyIiJUkieUdGJkYtSSJ6R0YmRi1GPEYtRi0= (factor@mm2persp@eq2mm)(eqn0): ici_persp:= elimifacu(%); ency(%); NyUqJiwmKiRJImFHNiIiIiUiIiMqJkkiYkdGJ0YpSSJjR0YnRikiIiIhIiJGJkYpKiYsJiokRitGKEYpKiZGJkYpRixGKUYtRi5GK0YpKiYsJiokRixGKEYpKiZGJkYpRitGKUYtRi5GLEYp SSI/RzYi tmp_inv:= bary2norm(cent)+(bary2norm(px)-bary2norm(cent))*rad2/(rad2-eqn0/(x+y+z)^2): #tmq:= (reduce@factor@evalmm)(%): (Vector@factor@subs)(defR2, %): #collect(-%/rotp(a^2), px, normal@expand, distributed); les fonctions funon, funinv, funsym (reduce@factor@evalmm@subs)(ency_, tmp_inv): funinv:= unapply(%,x,y,z)@op: funon:= unapply(subs(ency_, eqn0), x,y,z)@op: (reduce@subs)(ency_, reflection(cent,px)): funsym:= unapply(%,x,y,z)@op: Bien r\303\251gler le seuil... ou bien passer \303\240 20 chiffres Digits:=20: ici_on:= [seq](`if`((abs@funon)(xyz[j])<Float(1,-6),j,NULL),j=1..jmax); nops(%); NyYiIiQiIiciJSQzIiIlOzg= IiIl Les inverses-in-circle qqr:= table(): for j to jmax do if ff[j]=1 then next fi; tmp:= ency(funinv(xyz[j])): if tmp <>`?` then qqr[j]:= tmp; fi; od: # j:='j': ici_inv:= sort(map(op,[indices](qqr))); nops(%); bad_points=seq(`if`(qqr[qqr[j]]=j,NULL,j), j=ici_inv); 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 IiMpKg== L0krYmFkX3BvaW50c0c2IkYk On doit retrouver le nombre de points sur le cercle [seq](`if`(qqr[j]=j,j,NULL),j=ici_inv): nops(%); IiIl Les antipodaux qqr:= table(): for j in ici_on do tmp:= ency(funsym(xyz[j])): if tmp <>`?` then qqr[j]:= tmp; fi; od: j:='j': lesk:= sort(map(op,[indices](qqr))); nops(%); bad_points=seq(`if`(qqr[qqr[j]]=j,NULL,j), j=lesk); NyQiIiQiIic= IiIj L0krYmFkX3BvaW50c0c2IkYk Digits:=10: Il faut envoyer cela ***si besoin*** dans un r\303\251pertoire lisible et navigable if false then try close(fd); catch : end try; fd := open("/home/douillet/public_html/etc/alt_data.csv", WRITE): for j in lesk do fprintf(fd, """%d"";""%d""\134n", j, qqr[j]); od: close(fd); j:='j': fi:
<Text-field style="Heading 1" layout="Heading 1">Spieker +antipodie</Text-field> j:='j': num_cent:=10; cent:= pX(%); IiM1 NyUsJkkiY0c2IiIiIkkiYkdGJUYmLCZJImFHRiVGJkYkRiYsJkYnRiZGKUYm rad2:= subs(kitcircle, valR22, (r/2)^2 ); LCQqKiwoSSJiRzYiIiIiSSJhR0YmRidJImNHRiYhIiJGJywoRihGJ0YpRidGJUYqRicsKEYlRipGKUYqRihGJ0YnLChGKEYnRiVGJ0YpRidGKiNGKiIjOw== (factor@pp2uu)(cent): spie_uu:= (Vector@factor@subs)(defR2,%); ici_uu:=%: ency(%); LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpS0luUg== SSI/RzYi isolate(defR2, a+b-c): spie_rad:= (sqrt@factor@subs)(%, rad2) assuming a>0,b>0,c>0,R>0;ici_rad:=%: LCQqLEkiY0c2IiIiIkkiYkdGJUYmSSJhR0YlRiYsKEYoRiZGJ0YmRiRGJiEiIkkiUkdGJUYqI0YmIiIl subs(rho2=rad2, valR22, zipq(Vector(pu), ici_uu), eq_dou): eqn0:= sort(collect(%, px, factor, distributed), [x,y,z]); LC4qJiwuKiRJImFHNiIiIiMjIiIkIiM7KiZGJiIiIkkiY0dGJ0YtIyEiIiIiKSomRiZGLUkiYkdGJ0YtRi8qJkYzRi1GLkYtI0YqRjEqJEYuRigjISImRisqJEYzRihGN0YtSSJ4R0YnRihGLSoqLChGJkYtRjNGLUYuRi1GLSwoRjNGLUYmRi1GLiEiJEYtRjpGLUkieUdGJ0YtRi8qKkY8Ri0sKEYzRj5GJkYtRi5GLUYtRjpGLUkiekdGJ0YtRi8qJiwuRiVGN0YsRjVGMkYvRjRGL0Y2RjdGOUYpRi1GP0YoRi0qKkY8Ri0sKEYzRjBGJkYqRi5GMEYtRj9GLUZCRi0jRi1GMSomLC5GJUY3RixGL0YyRjVGNEYvRjZGKUY5RjdGLUZCRihGLQ== circlefunction:= subs(y=0,z=0,x=1,eqn0)/b/c;
<Text-field style="Heading 2" layout="Heading 2">antipodie</Text-field> _O1:= pX(3); _O2:= cent; NyUqJkkiYUc2IiIiIywoKiRGJEYmISIiKiRJImJHRiVGJiIiIiokSSJjR0YlRiZGLEYsKiZGK0YmLChGLUYsRihGLEYqRilGLComRi5GJiwoRihGLEYqRixGLUYpRiw= NyUsJkkiY0c2IiIiIkkiYkdGJUYmLCZJImFHRiVGJkYkRiYsJkYnRiZGKUYm (R*bary2norm(cent)- ici_rad*bary2norm(pX(3)))/(R-ici_rad): (reduce@FActor@evalmm)(%): _V:= (elimifacu@FActor@subs)(defR2, %); ency(%); NyUqJkkiYUc2IiIiIiwqKiZGJEYmSSJiR0YlRiYhIiIqJkYpRiZJImNHRiVGJiIiIyokRiRGLUYmKiZGJEYmRixGJkYqRiYsJComRilGJiwqRi8hIiNGK0YmRihGJiokRilGLUYqRiZGKiomRixGJiwqRihGLUYrRipGL0YqKiRGLEYtRiZGJg== IiV3OA== (R*bary2norm(cent) + ici_rad*bary2norm(pX(3)))/(R+ici_rad): (reduce@FActor@evalmm)(%): _U:= (elimifacu@FActor@subs)(defR2, %);ency(%); NyUqKEkiYUc2IiIiIiwoSSJiR0YlISIiSSJjR0YlRilGJEYmRiYsKiomRiRGJkYoRiZGJiomRihGJkYqRiYiIiMqJEYkRi5GJiomRiRGJkYqRiZGJkYmLCQqKEYoRiYsKkYtRiZGMEYuRixGJiokRihGLkYmRiYsKEYkRiZGKkYmRihGKUYmRiksJCooRipGJiwqRixGLkYtRiZGMEYmKiRGKkYuRiZGJiwoRihGJkYkRiZGKkYpRiZGKQ== IiRlKg== (reduce@factor@wedge)(wedge(_P,_U),wedge(_PP,_V)): collect(%, pp, factor): _Q:= Vector(xcollect(%, [rot3](-a+b+c))); LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpI1IpSD4= (elimifacu@factor@wedge)(wedge(_PP,_U),wedge(_P,_V)): collect(%, pp, factor): _QQ:= Vector(xcollect(-%, [rot3](-a+b+c))); (reduce@factor)(bary2norm(_Q)+bary2norm(_QQ))=cent; LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpM215YA== LzclLCZJImNHNiIiIiJJImJHRiZGJywmSSJhR0YmRidGJUYnLCZGKEYnRipGJ0Yj fac:=a^2: subs(zipq(pp, prm_cir(pdr)), _Q): _Qprm:= Vector(%); LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpOzdaPw== fac:=a^2: subs(zipq(pp, prm_cir(pdr)), _QQ): _QQprm:= Vector(%); LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpc0k/XQ== unapply(eqn0, x,y,z)@OP: map(factor@%, [_Q,_QQ,_Qprm,_QQprm]): subs(eqcircum(pp)=0, %);; NyYiIiFGI0YjRiM= fac:= b+c-a: unapply(convert(_Q,list),p,q,r)@op: tokim(%,pp): collect(%[1]/fac, pp, factor): xcollect(%, [a*b+2*b*c+a^2+a*c,p,a], factor); LCYqJiwmKiZJImJHNiIiIiJJInFHRidGKEYoKiZJImNHRidGKEkickdGJ0YoRihGKCwqKiZJImFHRidGKEYmRihGKComRiZGKEYrRigiIiMqJEYvRjFGKComRi9GKEYrRihGKEYoRigqJiwmKiYsJiokRiZGMUYoKiRGK0YxRihGKEYvRihGKComLCZGK0YoRiZGKEYoLCZGJkYoRishIiJGMUYoRihJInBHRidGKEYo fac:= 1: unapply(convert(_QQ,list),p,q,r)@op: tokim(%,pp): collect(%[1]/fac, pp, factor): xcollect(%, [-a*b+2*b*c+a^2-a*c,p,a], factor); LCYqJiwmKiZJImJHNiIiIiJJInFHRidGKCEiIiomSSJjR0YnRihJInJHRidGKEYqRigsKiomSSJhR0YnRihGJkYoRioqJkYmRihGLEYoIiIjKiRGMEYyRigqJkYwRihGLEYoRipGKEYoKiYsJiomLCYqJEYmRjJGKiokRixGMkYqRihGMEYoRigqJiwmRixGKEYmRihGKCwmRiZGKEYsRipGMkYoRihJInBHRidGKEYo
facxx, facyz:=1/16, (a+b+c)/8: j:='j': A(facxx)*Sum( simplify(coeff(eqn0,x,2)/facxx)*x^2,j)+ A(facyz)*Sum(simplify(coeff(coeff(eqn0,y),z)/facyz)*y*z,j): ici_eqn:= sort(%, [x,y,z,a,b,c]); LCYqJi1JIkFHNiI2IyMiIiIiIztGKS1JJFN1bUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJjYkKiYsLiokSSJhR0YmIiIjIiIkKiZGNEYpSSJiR0YmRikhIiMqJkY0RilJImNHRiZGKUY5KiRGOEY1ISImKiZGOEYpRjtGKSIiJyokRjtGNUY9RilJInhHRiZGNUkiakdGJkYpRikqJi1GJTYjLChGNCNGKSIiKUY4RkdGO0ZHRiktRiw2JCooLChGNEY2RjghIiJGO0ZNRilJInlHRiZGKUkiekdGJkYpRkJGKUYp (factor@mm2persp@eq2mm)(eqn0): ici_persp:= elimifacu(%); ency(%); NyUiIiJGI0Yj IiIj tmp_inv:= bary2norm(cent)+(bary2norm(px)-bary2norm(cent))*rad2/(rad2-eqn0/(x+y+z)^2): #tmq:= (reduce@factor@evalmm)(%): (Vector@factor@subs)(defR2, %): #collect(-%/rotp(a^2), px, normal@expand, distributed); les fonctions funon, funinv, funsym (reduce@factor@evalmm@subs)(ency_, tmp_inv): funinv:= unapply(%,x,y,z)@op: funon:= unapply(subs(ency_, eqn0), x,y,z)@op: (reduce@subs)(ency_, reflection(cent,px)): funsym:= unapply(%,x,y,z)@op: Bien r\303\251gler le seuil... ou bien passer \303\240 20 chiffres Digits:=20: ici_on:= [seq](`if`((abs@funon)(xyz[j])<Float(1,-6),j,NULL),j=1..jmax); nops(%); NyoiJU5JIiVPSSIlUEkiJVFJIiVSSSIlU0kiJVRJIiVVSQ== IiIp Les inverses-in-circle qqr:= table(): for j to jmax do if ff[j]=1 then next fi; tmp:= ency(funinv(xyz[j])): if tmp <>`?` then qqr[j]:= tmp; fi; od: # j:='j': ici_inv:= sort(map(op,[indices](qqr))); nops(%); bad_points=seq(`if`(qqr[qqr[j]]=j,NULL,j), j=ici_inv); NysiJT44IiVOSSIlT0kiJVBJIiVRSSIlUkkiJVNJIiVUSSIlVUk= IiIq L0krYmFkX3BvaW50c0c2IjYjIiU+OA== tmq: funinv(xyz[1319]): false667:=%/add(k,k=%); map(convert,%,rational); NyUkIjU0Ly1edihRcE1uJCEjPyQiNXVIJylHMkQpPkM+JEYlJCI1Pm02PzwoeTVUOCRGJQ== NyUjIiM9IiNcIyIkPiMiJCdvIyIkOiNGKA== true667:= xyz[667];map(convert,%,rational); NyUkIjUzLy1edihRcE1uJCEjPyQhNUg5ZEc5ZEdrcEAhIz4kIjUpUXBNbiQ9ZkgtR0Yo NyUjIiM9IiNcIyEkViMiJDciIyIlKD4jIiQleQ== (reduce@subs)(ency_, pX(667)): %/add(k, k=%); NyUjIiM9IiNcIyEkViMiJDciIyIlKD4jIiQleQ== On doit retrouver le nombre de points sur le cercle [seq](`if`(qqr[j]=j,j,NULL),j=ici_inv): nops(%); IiIp Les antipodaux qqr:= table(): for j in ici_on do tmp:= ency(funsym(xyz[j])): if tmp <>`?` then qqr[j]:= tmp; fi; od: j:='j': lesk:= sort(map(op,[indices](qqr))); nops(%); bad_points=seq(`if`(qqr[qqr[j]]=j,NULL,j), j=lesk); NyYiJU5JIiVPSSIlU0kiJVVJ IiIl L0krYmFkX3BvaW50c0c2IkYk Digits:=10: Il faut envoyer cela ***si besoin*** dans un r\303\251pertoire lisible et navigable if false then try close(fd); catch : end try; fd := open("/home/douillet/public_html/etc/alt_data.csv", WRITE): for j in lesk do fprintf(fd, """%d"";""%d""\134n", j, qqr[j]); od: close(fd); j:='j': fi:
<Text-field style="Heading 1" layout="Heading 1">orthocentroidal (new)</Text-field> j:='j': cent:= -(reduce@factor)(bary2norm(pX(2))+bary2norm(pX(4))); num_cent:=ency(%); NyUsLiomSSJiRzYiIiIjSSJjR0YmRiciIiUqJEYoRikhIiMqJEkiYUdGJkYpIiIiKiRGJUYpRisqJkYtRidGJUYnRi4qJkYtRidGKEYnRi4sLkYsRitGMUYpRi9GLkYqRitGMEYuRiRGLiwuRipGLkYsRitGMEYpRi9GK0YxRi5GJEYu IiQiUQ== rad2:= (factor@pytha)(cent, pX(2)); LCQqLCw2KiRJImFHNiIiIiciIiIqJkYmIiIlSSJiR0YnIiIjISIiKiZGJkYrSSJjR0YnRi1GLiomRiZGLUYsRitGLiooRiZGLUYsRi1GMEYtIiIkKiZGJkYtRjBGK0YuKiRGLEYoRikqJkYsRitGMEYtRi4qJkYsRi1GMEYrRi4qJEYwRihGKUYpLChGLEYpRiZGKUYwRi5GLiwoRiZGKUYsRilGMEYpRi4sKEYmRilGMEYpRixGLkYuLChGLEYuRjBGLkYmRilGLiNGLiIiKg== WW3; KiQsNiokSSJhRzYiIiInIiIiKiZGJSIiJUkiYkdGJiIiIyEiIiomRiVGKkkiY0dGJkYsRi0qJkYlRixGK0YqRi0qKEYlRixGK0YsRi9GLCIiJComRiVGLEYvRipGLSokRitGJ0YoKiZGK0YqRi9GLEYtKiZGK0YsRi9GKkYtKiRGL0YnRigjRihGLA== (factor@pp2uu)(cent): oc_uu:= (Vector@factor@subs)(defR2,%); ici_uu:=%: ency(%); LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpV1Zddg== SSI/RzYi subs(rho2=rad2, valR22, zipq(Vector(pu), ici_uu), eq_dou): eqn0:= sort(collect(%, px, factor, distributed), [x,y,z]); LC4qJiwoKiRJImFHNiIiIiMjIiIiIiIkKiRJImJHRidGKCMhIiJGKyokSSJjR0YnRihGLkYqSSJ4R0YnRihGKiooRjFGKEYyRipJInlHRidGKkYpKihGLUYoRjJGKkkiekdGJ0YqRikqJiwoRjBGLkYlRi5GLEYpRipGNEYoRioqKEYmRihGNEYqRjZGKkYpKiYsKEYlRi5GLEYuRjBGKUYqRjZGKEYq circlefunction:= subs(y=0,z=0,x=1,eqn0)/b/c; KigsKCokSSJhRzYiIiIjIyIiIiIiJCokSSJiR0YmRicjISIiRioqJEkiY0dGJkYnRi1GKUYsRi5GMEYu facxx, facyz:=1/3, 1/3: j:='j': A(facxx)*Sum( simplify(coeff(eqn0,x,2)/facxx)*x^2,j)+ A(facyz)*Sum(simplify(coeff(coeff(eqn0,y),z)/facyz)*y*z,j): ici_eqn:= sort(%, [a,b,c,x,y,z]); LCYqJi1JIkFHNiI2IyMiIiIiIiRGKS1JJFN1bUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJjYkKiYsKCokSSJhR0YmIiIjRikqJEkiYkdGJkY1ISIiKiRJImNHRiZGNUY4RilJInhHRiZGNUkiakdGJkYpRikqJkYkRiktRiw2JCooRjRGNUkieUdGJkYpSSJ6R0YmRilGPEYpRik= (factor@mm2persp@eq2mm)(eqn0): ici_persp:= elimifacu(%); ency(%); NyUqJCwqKiRJImFHNiIiIiUiIiMqJkYmRilJImJHRidGKSEiIyomRiZGKUkiY0dGJ0YpRiwqJkYrRilGLkYpISIiRjAsJCokLCpGL0YpRipGKSokRitGKEYsRi0iIiJGMEYwLCQqJCwqRi1GKUYvRikqJEYuRihGLEYqRjVGMEYw SSI/RzYi tmp_inv:= bary2norm(cent)+(bary2norm(px)-bary2norm(cent))*rad2/(rad2-eqn0/(x+y+z)^2): #tmq:= (reduce@factor@evalmm)(%): (Vector@factor@subs)(defR2, %): #collect(-%/rotp(a^2), px, normal@expand, distributed); les fonctions funon, funinv, funsym (reduce@factor@evalmm@subs)(ency_, tmp_inv): funinv:= unapply(%,x,y,z)@op: (reduce@factor@evalmm@subs)(enzy_, tmp_inv): zuninv:= unapply(%,x,y,z)@op: funon:= unapply(subs(ency_, eqn0), x,y,z)@op: (reduce@subs)(ency_, reflection(cent,px)): funsym:= unapply(%,x,y,z)@op: Bien r\303\251gler le seuil... ou bien passer \303\240 20 chiffres Digits:=20: ici_on:= [seq](`if`((abs@funon)(xyz[j])<Float(1,-6),j,NULL),j=1..jmax); nops(%); NyQiIiMiIiU= IiIj Les inverses-in-circle qqr:= table(): for j to jmax do if ff[j]=1 then next fi; tmp:= ency(funinv(xyz[j])): if tmp <>`?` then qqr[j]:= tmp; fi; od: # j:='j': ici_inv:= sort(map(op,[indices](qqr))); nops(%); bad_points=seq(`if`(qqr[qqr[j]]=j,NULL,j), j=ici_inv); 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 IiMjKg== L0krYmFkX3BvaW50c0c2IkYk for j in ici_inv do zuninv(zxyz[j]); %/add(k,k=%)-zxyz[qqr[j]]; if add(abs(k),k=%) > Float(1,-10) then print(j) fi; od: IiVHTg== IiVXTg== zuninv(zxyz[3528]); evalf(%/add(k,k=%),10); NyUkITRFNWtENWsmPSJ5JiEjOCQhNSd6KUhSZjojb0k3IkYlJCI1eUUzQSlSXD9WdCNGJQ== NyUkISt1bngmZiYhIzUkISswLTAoMyIhIiokIiskKXlpWUVGKA== [-.5595776774, -1.087050205, 2.646627883] qqr[3544]; IiVHTg== On doit retrouver le nombre de points sur le cercle [seq](`if`(qqr[j]=j,j,NULL),j=ici_inv): nops(%); IiIj Les antipodaux qqr:= table(): for j in ici_on do tmp:= ency(funsym(xyz[j])): if tmp <>`?` then qqr[j]:= tmp; fi; od: j:='j': lesk:= sort(map(op,[indices](qqr))); nops(%); bad_points=seq(`if`(qqr[qqr[j]]=j,NULL,j), j=lesk); NyQiIiMiIiU= IiIj L0krYmFkX3BvaW50c0c2IkYk Digits:=10: Il faut envoyer cela ***si besoin*** dans un r\303\251pertoire lisible et navigable if false then try close(fd); catch : end try; fd := open("/home/douillet/public_html/etc/alt_data.csv", WRITE): for j in lesk do fprintf(fd, """%d"";""%d""\134n", j, qqr[j]); od: close(fd); j:='j': fi:
<Text-field style="Heading 1" layout="Heading 1">Fuhrmann (new)</Text-field> j:='j': cent:= -(reduce@factor)(bary2norm(pX(4))+bary2norm(pX(8))); num_cent:=ency(%); NyUsOCokSSJhRzYiIiIlIiIiKiZGJSIiJEkiY0dGJkYoISIiKiZGJUYqSSJiR0YmRihGLCooRiUiIiNGLkYoRitGKEYwKihGJUYoRi5GMEYrRihGLComRitGKkYlRihGKCooRiVGKEYuRihGK0YwRiwqJkYlRihGLkYqRigqJkYuRjBGK0YwRjAqJEYrRidGLCokRi5GJ0YsLDhGJEYsRi1GKComRiVGMEYrRjBGMEYvRixGMUYwRjRGLEYzRixGNkYsKiZGLkYqRitGKEYsRjdGKComRitGKkYuRihGKCw4RiRGLEYpRigqJkYlRjBGLkYwRjBGL0YsRjJGLEYzRjBGMUYsRjZGKEY6RihGN0YsRjtGLA== IiRiJA== rad2:= (factor@pytha)(cent, pX(4)); LCQqMkkiYUc2IiIiIkkiY0dGJUYmSSJiR0YlRiYsNiokRigiIiRGJiomRigiIiNGJ0YmISIiKiZGKEYmRidGLUYuKiRGJ0YrRiYqJkYkRiZGKEYtRi4qKEYkRiZGKEYmRidGJkYrKiZGJEYmRidGLUYuKiZGKEYmRiRGLUYuKiZGJ0YmRiRGLUYuKiRGJEYrRiZGJiwoRihGJkYkRiZGJ0YuRi4sKEYkRiZGKEYmRidGJkYuLChGJEYmRidGJkYoRi5GLiwoRihGLkYnRi5GJEYmRi5GLg== ruleW:= WW4^2=W4^2; Lyw2KiRJImJHNiIiIiQiIiIqJkYlIiIjSSJjR0YmRighIiIqJkYlRihGK0YqRiwqJEYrRidGKComSSJhR0YmRihGJUYqRiwqKEYwRihGJUYoRitGKEYnKiZGMEYoRitGKkYsKiZGJUYoRjBGKkYsKiZGK0YoRjBGKkYsKiRGMEYnRigqJEkjVzRHRiZGKg== (sqrt@subs)(ruleW, apbpc, rad2): fuhr_rad:= simplify(%) assuming R>0,W4>0; KihJI1c0RzYiIiIiSSJSR0YkRiUqKEkiYUdGJCEiIkkiY0dGJEYpSSJiR0YkRikjRiUiIiM= (factor@pp2uu)(cent): fuhr_uu:= (Vector@factor@subs)(defR2,%); ici_uu:=%: ency(%); LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpI3p3VCM= SSI/RzYi Plus bo (FActor@simplify)( subs(apbpc,fuhr_uu), {ruleW}): tmp:= collect(%, [W4, R], factor):; isolate(ruleW, a^3); collect(subs(%, tmp[3]), [R,W4], factor); sort(rot(%), [a,b,c]): collect(%, [R,W4], factor): fuhr_uu:= Vector([rot3](%)); (FActor@subs)(defR2, W4=WW4, %-ici_uu); LyokSSJhRzYiIiIkLDYqJEkjVzRHRiUiIiMiIiIqJEkiYkdGJUYmISIiKiZJImNHRiVGK0YtRipGKyomRi1GK0YwRipGKyokRjBGJkYuKiZGJEYrRi1GKkYrKihGJEYrRi1GK0YwRishIiQqJkYkRitGMEYqRisqJkYtRitGJEYqRisqJkYwRitGJEYqRis= KiYsJiosLCoqJEkiYUc2IiIiIyIiIiokSSJiR0YoRilGKiokSSJjR0YoRikhIiIqJkYnRipGLEYqRi9GKkYuRi9GJyEiI0YsRjFJI1c0R0YoRilGLyooLChGJkYqRitGKkYtRi9GKkYnRi9GLEYvRipGKkkiUkdGKEYp LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpP2xuOg== LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpJ1xGKnA= subs(rho2=rad2, valR22, zipq(Vector(pu), ici_uu), eq_dou): eqn0:= sort(collect(%, px, factor, distributed), [x,y,z]); LC4qKiwoKiRJImFHNiIiIiMiIiIqJEkiYkdGJ0YoISIiKiRJImNHRidGKEYsRilGJkYpLChGJkYpRitGKUYuRilGLEkieEdGJ0YoRikqKiwsKiRGJiIiJEYpKiZGK0YpRiZGKEYsKiZGJkYpRitGKEYsKiRGLkY0RikqJEYrRjRGKUYpRi9GLEYwRilJInlHRidGKUYpKiosLEYzRikqJkYuRilGJkYoRiwqJkYmRilGLkYoRixGN0YpRjhGKUYpRi9GLEYwRilJInpHRidGKUYpKiosKEYtRilGJUYpRipGLEYpRitGKUYvRixGOUYoRiwqKiwsRjNGKSomRitGKUYuRihGLComRi5GKUYrRihGLEY3RilGOEYpRilGL0YsRjlGKUY+RilGKSoqRi5GKSwoRiVGKUYqRilGLUYsRilGL0YsRj5GKEYs circlefunction:= subs(y=0,z=0,x=1,eqn0)/b/c; facxx, facyz:=1/(a+b+c) $2: j:='j': A(facxx)*Sum( simplify(coeff(eqn0,x,2)/facxx)*x^2,j)+ A(facyz)*Sum(simplify(coeff(coeff(eqn0,y),z)/facyz)*y*z,j): ici_eqn:= sort(%, [a,b,c,x,y,z]); LCYqJi1JIkFHNiI2IyokLChJImFHRiYiIiJJImJHRiZGK0kiY0dGJkYrISIiRistSSRTdW1HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2JCooLCgqJEYqIiIjRisqJEYsRjhGLiokRi1GOEYuRitGKkYrSSJ4R0YmRjhJImpHRiZGK0YrKiZGJEYrLUYwNiQqKCwsKiRGKiIiJEYrKiRGLEZDRisqJkYsRjhGLUYrRi4qJkYsRitGLUY4Ri4qJEYtRkNGK0YrSSJ5R0YmRitJInpHRiZGK0Y8RitGKw== (factor@mm2persp@eq2mm)(eqn0): ici_persp:= elimifacu(%); ency(%); 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 SSI/RzYi tmp_inv:= bary2norm(cent)+(bary2norm(px)-bary2norm(cent))*rad2/(rad2-eqn0/(x+y+z)^2): #tmq:= (reduce@factor@evalmm)(%): (Vector@factor@subs)(defR2, %): #collect(-%/rotp(a^2), px, normal@expand, distributed); les fonctions funon, funinv, funsym (reduce@factor@evalmm@subs)(ency_, tmp_inv): funinv:= unapply(%,x,y,z)@op: funon:= unapply(subs(ency_, eqn0), x,y,z)@op: (reduce@subs)(ency_, reflection(cent,px)): funsym:= unapply(%,x,y,z)@op: Bien r\303\251gler le seuil... ou bien passer \303\240 20 chiffres Digits:=20: ici_on:= [seq](`if`((abs@funon)(xyz[j])<Float(1,-6),j,NULL),j=1..jmax); nops(%); NyQiIiUiIik= IiIj Les inverses-in-circle qqr:= table(): for j to jmax do if ff[j]=1 then next fi; tmp:= ency(funinv(xyz[j])): if tmp <>`?` then qqr[j]:= tmp; fi; od: # j:='j': ici_inv:= sort(map(op,[indices](qqr))); nops(%); bad_points=seq(`if`(qqr[qqr[j]]=j,NULL,j), j=ici_inv); Ny4iIiIiIiUiIikiIzYiI3MiIyEpIiVQPSIldkMiJT5NIiVNTSIlT00iJVtN IiM3 L0krYmFkX3BvaW50c0c2IkYk On doit retrouver le nombre de points sur le cercle [seq](`if`(qqr[j]=j,j,NULL),j=ici_inv): nops(%); IiIj Les antipodaux qqr:= table(): for j in ici_on do tmp:= ency(funsym(xyz[j])): if tmp <>`?` then qqr[j]:= tmp; fi; od: j:='j': lesk:= sort(map(op,[indices](qqr))); nops(%); bad_points=seq(`if`(qqr[qqr[j]]=j,NULL,j), j=lesk); NyQiIiUiIik= IiIj L0krYmFkX3BvaW50c0c2IkYk Digits:=10: Il faut envoyer cela ***si besoin*** dans un r\303\251pertoire lisible et navigable if false then try close(fd); catch : end try; fd := open("/home/douillet/public_html/etc/alt_data.csv", WRITE): for j in lesk do fprintf(fd, """%d"";""%d""\134n", j, qqr[j]); od: close(fd); j:='j': fi:
<Text-field style="Heading 1" layout="Heading 1">Lemoine 1 (new)</Text-field> j:='j': num_cent:=182; cent:= pX(%); IiQjPQ== NyUqJkkiYUc2IiIiIywoKiRGJCIiJSIiIiomRiRGJiwmKiRJImJHRiVGJkYqKiRJImNHRiVGJkYqRiohIiIqJkYuRiZGMEYmISIjRioqJkYuRiYsKCokRi5GKUYqKiZGLkYmLCZGL0YqKiRGJEYmRipGKkYxKiZGJEYmRjBGJkYzRioqJkYwRiYsKCokRjBGKUYqKiZGMEYmLCZGOUYqRi1GKkYqRjEqJkYkRiZGLkYmRjNGKg== rad2:= subs(kitcircle, valR22, (R/cos(omega)/2)^2 ); LCQqNEkiYUc2IiIiI0kiYkdGJUYmSSJjR0YlRiYsKEYnIiIiRiRGKkYoISIiRissKEYkRipGJ0YqRihGKkYrLChGJEYqRihGKkYnRitGKywoRidGK0YoRitGJEYqRissKCokRiRGJkYqKiRGJ0YmRioqJEYoRiZGKiEiIywoKiZGJEYmRidGJkYqKiZGJEYmRihGJkYqKiZGJ0YmRihGJkYqRipGKw== ruleW:= WW1^2=W1^2; LywoKiZJImFHNiIiIiNJImJHRiZGJyIiIiomRiVGJ0kiY0dGJkYnRikqJkYoRidGK0YnRikqJEkjVzFHRiZGJw== (factor@pp2uu)(cent): lem1_uu:= (Vector@factor@subs)(defR2,%); ici_uu:=%: ency(%); LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpb0A1Uw== SSI/RzYi subs(apbpc, ruleW, rad2): lem1_rad:= simplify(sqrt(%), symbolic); KihJIlJHNiIiIiIsKCokSSJhR0YkIiIjRiUqJEkiYkdGJEYpRiUqJEkiY0dGJEYpRiUhIiJJI1cxR0YkRiU= subs(rho2=rad2, valR22, zipq(Vector(pu), ici_uu), eq_dou): eqn0:= sort(collect(%, px, factor, distributed), [x,y,z]); LC4qLCwmKiRJImJHNiIiIiMiIiIqJEkiY0dGJ0YoRilGKSwoKiRJImFHRidGKEYpRiVGKUYqRikhIiNGJkYoRitGKEkieEdGJ0YoISIiKixGK0YoLCoqJkYuRihGK0YoRikqJkYuRihGJkYoRigqJkYmRihGK0YoRikqJEYrIiIlRilGKUYsRi9GMEYpSSJ5R0YnRilGKSosRiZGKCwqRjRGKEY1RikqJEYmRjhGKUY2RilGKUYsRi9GMEYpSSJ6R0YnRilGKSosRitGKEYuRigsJkYqRilGLUYpRilGLEYvRjlGKEYxKiwsKiokRi5GOEYpRjVGKUY0RilGNkYoRilGLEYvRi5GKEY5RilGPUYpRikqLEYmRihGLkYoLCZGLUYpRiVGKUYpRixGL0Y9RihGMQ== circlefunction:= subs(y=0,z=0,x=1,eqn0)/b/c; facxx, facyz:=1/(a^2+b^2+c^2)^2 $2: j:='j': A(facxx)*Sum( simplify(coeff(eqn0,x,2)/facxx)*x^2,j)+ A(facyz)*Sum(simplify(coeff(coeff(eqn0,y),z)/facyz)*y*z,j): ici_eqn:= sort(%, [a,b,c,x,y,z]); LCYqJi1JIkFHNiI2IyokLCgqJEkiYUdGJiIiIyIiIiokSSJiR0YmRixGLSokSSJjR0YmRixGLSEiI0YtLUkkU3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiQsJCoqLCZGLkYtRjBGLUYtRi9GLEYxRixJInhHRiZGLCEiIkkiakdGJkYtRi0qJkYkRi0tRjQ2JCoqLCoqJEYrIiIlRi0qJkYrRixGL0YsRi0qJkYrRixGMUYsRi0qJkYvRixGMUYsRixGLUYrRixJInlHRiZGLUkiekdGJkYtRj5GLUYt (factor@mm2persp@eq2mm)(eqn0): ici_persp:= elimifacu(%); ency(%); NyUqJiwoKiZJImFHNiIiIiNJImJHRidGKEYoKiZGJkYoSSJjR0YnRihGKComRilGKEYrRigiIiIhIiJGJkYoKiYsKEYqRi1GJUYoRixGKEYuRilGKComLChGKkYoRiVGLUYsRihGLkYrRig= SSI/RzYi tmp_inv:= bary2norm(cent)+(bary2norm(px)-bary2norm(cent))*rad2/(rad2-eqn0/(x+y+z)^2): #tmq:= (reduce@factor@evalmm)(%): (Vector@factor@subs)(defR2, %): #collect(-%/rotp(a^2), px, normal@expand, distributed); les fonctions funon, funinv, funsym (reduce@factor@evalmm@subs)(ency_, tmp_inv): funinv:= unapply(%,x,y,z)@op: funon:= unapply(subs(ency_, eqn0), x,y,z)@op: (reduce@subs)(ency_, reflection(cent,px)): funsym:= unapply(%,x,y,z)@op: Bien r\303\251gler le seuil... ou bien passer \303\240 20 chiffres Digits:=20: ici_on:= [seq](`if`((abs@funon)(xyz[j])<Float(1,-6),j,NULL),j=1..jmax); nops(%); NyQiJWk7IiVqOw== IiIj Les inverses-in-circle qqr:= table(): for j to jmax do if ff[j]=1 then next fi; tmp:= ency(funinv(xyz[j])): if tmp <>`?` then qqr[j]:= tmp; fi; od: # j:='j': ici_inv:= sort(map(op,[indices](qqr))); nops(%); bad_points=seq(`if`(qqr[qqr[j]]=j,NULL,j), j=ici_inv); NzIiIiQiIiciI0siI1IiJHIkIiRzJCIlaTsiJWo7IiUobyIiJSlvIiIlInAiIiUjcCIiJWNDIiVlQyIlaEMiJWlD IiM7 L0krYmFkX3BvaW50c0c2IkYk On doit retrouver le nombre de points sur le cercle [seq](`if`(qqr[j]=j,j,NULL),j=ici_inv): nops(%); IiIj Les antipodaux qqr:= table(): for j in ici_on do tmp:= ency(funsym(xyz[j])): if tmp <>`?` then qqr[j]:= tmp; fi; od: j:='j': lesk:= sort(map(op,[indices](qqr))); nops(%); bad_points=seq(`if`(qqr[qqr[j]]=j,NULL,j), j=lesk); NyQiJWk7IiVqOw== IiIj L0krYmFkX3BvaW50c0c2IkYk Digits:=10: Il faut envoyer cela ***si besoin*** dans un r\303\251pertoire lisible et navigable if false then try close(fd); catch : end try; fd := open("/home/douillet/public_html/etc/alt_data.csv", WRITE): for j in lesk do fprintf(fd, """%d"";""%d""\134n", j, qqr[j]); od: close(fd); j:='j': fi:
<Text-field style="Heading 1" layout="Heading 1">Lemoine 2 (new)</Text-field> j:='j': num_cent:=6; cent:= pX(%); IiIn NyUqJEkiYUc2IiIiIyokSSJiR0YlRiYqJEkiY0dGJUYm rad2:= subs(kitcircle, valR22, (a*b*c/(a^2+b**2+c**2))^2 ); KipJImFHNiIiIiNJImJHRiRGJUkiY0dGJEYlLCgqJEYjRiUiIiIqJEYmRiVGKiokRidGJUYqISIj ruleW:= WW1^2=W1^2; LywoKiZJImFHNiIiIiNJImJHRiZGJyIiIiomRiVGJ0kiY0dGJkYnRikqJkYoRidGK0YnRikqJEkjVzFHRiZGJw== (factor@pp2uu)(cent): lem2_uu:= (Vector@factor@subs)(defR2,%); ici_uu:=%: ency(%); LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpYz1XQw== SSI/RzYi subs(rho2=rad2, valR22, zipq(Vector(pu), ici_uu), eq_dou): eqn0:= sort(collect(%, px, factor, distributed), [x,y,z]); LC4qLEkiYkc2IiIiI0kiY0dGJUYmLCgqJEkiYUdGJUYmIiIiKiRGJEYmISIiKiRGJ0YmRi1GKywoRilGK0YsRitGLkYrISIjSSJ4R0YlRiZGJiosRidGJiwqKiZGKkYmRiRGJiEiJyokRiQiIiVGKyokRipGN0YrKiRGJ0Y3Ri1GK0YvRjBGMUYrSSJ5R0YlRitGLSosRiRGJiwqRjhGKyomRipGJkYnRiZGNUY2Ri1GOUYrRitGL0YwRjFGK0kiekdGJUYrRi0qLEYqRiZGJ0YmLChGLkYrRilGK0YsRi1GK0YvRjBGOkYmRjAqLEYqRiYsKiomRiRGJkYnRiYiIidGOUYtRjZGLUY4RitGK0YvRjBGOkYrRj5GK0YrKixGKkYmRiRGJiwoRilGK0YsRitGLkYtRitGL0YwRj5GJkYw circlefunction:= subs(y=0,z=0,x=1,eqn0)/b/c; facxx, facyz:=2/(a^2+b^2+c^2)^2, 1/(a^2+b^2+c^2)^2: j:='j': A(facxx)*Sum( simplify(coeff(eqn0,x,2)/facxx)*x^2,j)+ A(facyz)*Sum(simplify(coeff(coeff(eqn0,y),z)/facyz)*y*z,j): ici_eqn:= sort(%, [a,b,c,x,y,z]); LCYqJi1JIkFHNiI2IywkKiQsKCokSSJhR0YmIiIjIiIiKiRJImJHRiZGLUYuKiRJImNHRiZGLUYuISIjRi1GLi1JJFN1bUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJjYkKiosKEYrRi5GLyEiIkYxRjxGLkYwRi1GMkYtSSJ4R0YmRi1JImpHRiZGLkYuKiYtRiU2I0YpRi4tRjU2JCoqLCoqJEYsIiIlRi4qJEYwRkdGPComRjBGLUYyRi0iIicqJEYyRkdGPEYuRixGLUkieUdGJkYuSSJ6R0YmRi5GPkYuRi4= (factor@mm2persp@eq2mm)(eqn0): ici_persp:= elimifacu(%); ency(%); NyUqJiwuKiRJImFHNiIiIiUiIiQqJkYmIiIjSSJjR0YnRishIiUqJkYmRitJImJHRidGK0YtKiZGL0YrRixGKyEiIyokRixGKCIiIiokRi9GKEYzISIiRiZGKyomLC5GJUYzRi5GLUYqRjFGNEYpRjBGLUYyRjNGNUYvRisqJiwuRiVGM0YqRi1GLkYxRjJGKUYwRi1GNEYzRjVGLEYr SSI/RzYi tmp_inv:= bary2norm(cent)+(bary2norm(px)-bary2norm(cent))*rad2/(rad2-eqn0/(x+y+z)^2): #tmq:= (reduce@factor@evalmm)(%): (Vector@factor@subs)(defR2, %): #collect(-%/rotp(a^2), px, normal@expand, distributed); les fonctions funon, funinv, funsym (reduce@factor@evalmm@subs)(ency_, tmp_inv): funinv:= unapply(%,x,y,z)@op: funon:= unapply(subs(ency_, eqn0), x,y,z)@op: (reduce@subs)(ency_, reflection(cent,px)): funsym:= unapply(%,x,y,z)@op: Bien r\303\251gler le seuil... ou bien passer \303\240 20 chiffres Digits:=20: ici_on:= [seq](`if`((abs@funon)(xyz[j])<Float(1,-6),j,NULL),j=1..jmax); nops(%); NyQiJW07IiVuOw== IiIj Les inverses-in-circle qqr:= table(): for j to jmax do if ff[j]=1 then next fi; tmp:= ency(funinv(xyz[j])): if tmp <>`?` then qqr[j]:= tmp; fi; od: # j:='j': ici_inv:= sort(map(op,[indices](qqr))); nops(%); bad_points=seq(`if`(qqr[qqr[j]]=j,NULL,j), j=ici_inv); NzAiIiQiJHcmIiU7OCIlXjgiJXE6IiVtOyIlbjsiJSJwIiIlI3AiIiVeQyIlX0MiJSNwIyIlXEkiJXBM IiM5 L0krYmFkX3BvaW50c0c2IjYkIiUjcCMiJXBM qqr[2692]; funinv(xyz[2692]): false788:= %/add(k,k=%); map(convert,%,rational); true788:= xyz[788]; ff[788]; enc_dat[788]/subs(ency_, fac_ency); IiQpeQ== NyUkIjVdXF4/IUhKdkhpIiEjPyQiNU4lcEwjMykzKCo9KlFGJSQiNTpjNmMsKmZGXlslRiU= NyUjIit5cWM2NyIrRicpNGx1IyIrMEMpKTM2IitKej9cRyMiKzUpb3ImPSIrNm9zU1Q= NyUkIjVWJmY9UkRAdDwxIiEjPiQhNVVsKnojKnBNXmQkW0YlJCI1KipwOE9YTSJ5UngkRiU= IiIi JCI1WXJSNG5MYChIaSIhIz8= _i:= 3369: _j:= qqr[_i]; funinv(xyz[_i]): false||_j:= %/add(k,k=%); map(convert,%,rational); true||_j:= xyz[_j]; ff[_j]; #enc_dat[788]/subs(ency_, fac_ency); IiMqKQ== NyUkIjVsMCZbLUZLSTFHIiEjPyQiNSlSLENVLjlgciZHRiUkIjVOIVtGYnBgO0EnZUYl NyUjIitYK3E0NyIrYCpIaFcqIyIrXVdeUEAiK1xPRiJbKCMiKj06Mz8pIit0dCMqKVIi NyUkIjVsPj5uZ2QuaiFHIiEjPyQiNTFVZSg0eC8scl4jRiUkIjVIUUFObyVmb0E/J0Yl IiIh On doit retrouver le nombre de points sur le cercle [seq](`if`(qqr[j]=j,j,NULL),j=ici_inv): nops(%); IiIj Les antipodaux qqr:= table(): for j in ici_on do tmp:= ency(funsym(xyz[j])): if tmp <>`?` then qqr[j]:= tmp; fi; od: j:='j': lesk:= sort(map(op,[indices](qqr))); nops(%); bad_points=seq(`if`(qqr[qqr[j]]=j,NULL,j), j=lesk); NyQiJW07IiVuOw== IiIj L0krYmFkX3BvaW50c0c2IkYk Digits:=10: Il faut envoyer cela ***si besoin*** dans un r\303\251pertoire lisible et navigable if false then try close(fd); catch : end try; fd := open("/home/douillet/public_html/etc/alt_data.csv", WRITE): for j in lesk do fprintf(fd, """%d"";""%d""\134n", j, qqr[j]); od: close(fd); j:='j': fi:
<Text-field style="Heading 1" layout="Heading 1">sine-triple-angle (new)</Text-field> j:='j': num_cent:=49; cent:= pX(%); IiNc NyUqKEkiYUc2IiIiJSwoKiRGJCIiIyEiIiokSSJiR0YlRikiIiIqJEkiY0dGJUYpRi1GLSwuKiRGJEYmRi0qJkYkRilGLEYpISIjKiZGJEYpRi9GKUYzKiRGLEYmRi0qJkYsRilGL0YpRioqJEYvRiZGLUYtKihGLEYmLChGLkYtRihGLUYrRipGLSwuRjVGLUY2RjNGMkYzRjdGLUY0RipGMUYtRi0qKEYvRiYsKEYoRi1GK0YtRi5GKkYtLC5GN0YtRjRGM0Y2RjNGMUYtRjJGKkY1Ri1GLQ== (R/(1+8*cos(A)*cos(B)*cos(C)))^2: rad2:= (factor@subs)(kashi, defR2,%); ; LCQqMkkiYUc2IiIiJ0kiYkdGJUYmSSJjR0YlRiYsKEYnIiIiRiRGKkYoISIiRissKEYkRipGJ0YqRihGKkYrLChGJEYqRihGKkYnRitGKywoRidGK0YoRitGJEYqRissNiooRiQiIiNGJ0YxRihGMUYqKiRGJEYmRioqJkYkIiIlRidGMUYrKiZGJEY0RihGMUYrKiZGJEYxRidGNEYrKiRGJ0YmRioqJkYnRjRGKEYxRisqJkYkRjFGKEY0RisqJkYnRjFGKEY0RisqJEYoRiZGKiEiI0Yr ruleW:= WW3^2=W3^2; Lyw2KiRJImFHNiIiIiciIiIqJkYlIiIlSSJiR0YmIiIjISIiKiZGJUYqSSJjR0YmRixGLSomRiVGLEYrRipGLSooRiVGLEYrRixGL0YsIiIkKiZGJUYsRi9GKkYtKiRGK0YnRigqJkYrRipGL0YsRi0qJkYrRixGL0YqRi0qJEYvRidGKCokSSNXM0dGJkYs (factor@pp2uu)(cent): sta_uu:= (Vector@factor@subs)(defR2,%); ici_uu:=%: ency(%); LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpNzwkcCQ= SSI/RzYi rad2; numer(%)/subs(isolate(ruleW, a^6), apbpc, denom(%)): sta_rad:= map(sqrt,%) assuming a>0,b>0,c>0,R>0,-2*a^2*b^2*c^2+W3^2>0; LCQqMkkiYUc2IiIiJ0kiYkdGJUYmSSJjR0YlRiYsKEYnIiIiRiRGKkYoISIiRissKEYkRipGJ0YqRihGKkYrLChGJEYqRihGKkYnRitGKywoRidGK0YoRitGJEYqRissNiooRiQiIiNGJ0YxRihGMUYqKiRGJEYmRioqJkYkIiIlRidGMUYrKiZGJEY0RihGMUYrKiZGJEYxRidGNEYrKiRGJ0YmRioqJkYnRjRGKEYxRisqJkYkRjFGKEY0RisqJkYnRjFGKEY0RisqJEYoRiZGKiEiI0Yr KixJImFHNiIiIiNJImJHRiRGJUkiY0dGJEYlSSJSR0YkIiIiLCYqKEYjRiVGJkYlRidGJSEiIyokSSNXM0dGJEYlRikhIiI= subs(rho2=rad2, valR22, zipq(Vector(pu), ici_uu), eq_dou): eqn0:= sort(collect(%, px, factor, distributed), [x,y,z]); 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 circlefunction:= subs(y=0,z=0,x=1,eqn0)/b/c; facxx, facyz:=1/(a^6-a^4*b^2-a^4*c^2-a^2*b^4+a^2*b^2*c^2-a^2*c^4+b^6-b^4*c^2-b^2*c^4+c^6)^2 $2: j:='j': A(facxx)*Sum( factor(coeff(eqn0,x,2)/facxx)*x^2,j)+ A(facyz)*Sum(factor(coeff(coeff(eqn0,y),z)/facyz)*y*z,j): ici_eqn:= sort(%, [a,b,c,x,y,z]); 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 (factor@mm2persp@eq2mm)(eqn0): ici_persp:= elimifacu(%); ency(%); NyUqJkkiYUc2IiIiJSw8KiRGJCIiKSIiIiomRiQiIidJImJHRiUiIiMhIiIqJkYkRi5GLUYsRioqJEYtRilGLyomRiRGLEkiY0dGJUYuRi8qKEYzRi5GLUYuRiRGJkYvKihGM0YuRi1GJkYkRi5GLyomRi1GLEYzRi5GJiooRjNGJkYtRi5GJEYuRi8qJkYtRiZGM0YmISInKiZGJEYuRjNGLEYqKiZGLUYuRjNGLEYmKiRGM0YpRi9GLywkKiZGLUYmLDxGKEYqRitGL0YwRipGMUYvRjIhIiVGNEYqRjVGKkY2RioqJkYkRiZGM0YmRixGN0YqRjpGQEY7Ri9GPEYqRi9GLywkKiZGM0YmLDxGKEYqRitGQComRiRGJkYtRiZGLEYwRkBGMUYqRjJGL0Y0RipGNUYqRjZGL0Y3RipGOkYqRjtGKkY8Ri9GL0Yv SSI/RzYi tmp_inv:= bary2norm(cent)+(bary2norm(px)-bary2norm(cent))*rad2/(rad2-eqn0/(x+y+z)^2): #tmq:= (reduce@factor@evalmm)(%): (Vector@factor@subs)(defR2, %): #collect(-%/rotp(a^2), px, normal@expand, distributed); les fonctions funon, funinv, funsym (reduce@factor@evalmm@subs)(ency_, tmp_inv): funinv:= unapply(%,x,y,z)@op: funon:= unapply(subs(ency_, eqn0), x,y,z)@op: (reduce@subs)(ency_, reflection(cent,px)): funsym:= unapply(%,x,y,z)@op: Bien r\303\251gler le seuil... ou bien passer \303\240 20 chiffres Digits:=20: ici_on:= [seq](`if`((abs@funon)(xyz[j])<Float(1,-6),j,NULL),j=1..jmax); nops(%); NygiJVZJIiVXSSIlWEkiJVlJIiVaSSIlW0k= IiIn Les inverses-in-circle qqr:= table(): for j to jmax do if ff[j]=1 then next fi; tmp:= ency(funinv(xyz[j])): if tmp <>`?` then qqr[j]:= tmp; fi; od: # j:='j': ici_inv:= sort(map(op,[indices](qqr))); nops(%); bad_points=seq(`if`(qqr[qqr[j]]=j,NULL,j), j=ici_inv); NygiJVZJIiVXSSIlWEkiJVlJIiVaSSIlW0k= IiIn L0krYmFkX3BvaW50c0c2IkYk On doit retrouver le nombre de points sur le cercle [seq](`if`(qqr[j]=j,j,NULL),j=ici_inv): nops(%); IiIn Les antipodaux qqr:= table(): for j in ici_on do tmp:= ency(funsym(xyz[j])): if tmp <>`?` then qqr[j]:= tmp; fi; od: j:='j': lesk:= sort(map(op,[indices](qqr))); nops(%); bad_points=seq(`if`(qqr[qqr[j]]=j,NULL,j), j=lesk); NyQiJVZJIiVaSQ== IiIj L0krYmFkX3BvaW50c0c2IkYk Digits:=10: Il faut envoyer cela ***si besoin*** dans un r\303\251pertoire lisible et navigable if false then try close(fd); catch : end try; fd := open("/home/douillet/public_html/etc/alt_data.csv", WRITE): for j in lesk do fprintf(fd, """%d"";""%d""\134n", j, qqr[j]); od: close(fd); j:='j': fi:
<Text-field style="Heading 1" layout="Heading 1">Apollonius (new)</Text-field> j:='j': num_cent:=970; cent:= pX(%); IiRxKg== NyUqJkkiYUc2IiIiIywqKiZGJCIiJCwmSSJjR0YlIiIiSSJiR0YlRixGJkYsKihGKkYsLCYqJEYtRiZGLCokRitGJkYsRixGJEYmRiwqJiwqKiRGLSIiJSEiIiomRi1GKUYrRiwhIiMqJkYrRilGLUYsRjgqJEYrRjVGNkYsRiRGLEYsKiZGKkYsLCZGNEYsRjpGLEYsRjZGLComRi1GJiwqKiZGLUYpLCZGJEYsRitGLEYmRiwqKEZARiwsJkYxRiwqJEYkRiZGLEYsRi1GJkYsKiYsKkY6RjYqJkYrRilGJEYsRjgqJkYkRilGK0YsRjgqJEYkRjVGNkYsRi1GLEYsKiZGQEYsLCZGOkYsRkhGLEYsRjZGLComRitGJiwqKiZGK0YpLCZGLUYsRiRGLEYmRiwqKEZORiwsJkZDRixGMEYsRixGK0YmRiwqJiwqRkhGNiomRiRGKUYtRixGOComRiRGLEYtRilGOEY0RjZGLEYrRixGLComRk5GLCwmRkhGLEY0RixGLEY2Riw= apol_rad:= (factor@subs)(kitcircle, valR22, (r^2+s^2)/4/r); LCQqLEkiUkc2IiIiIiwwKiZJImJHRiUiIiNJImNHRiVGJkYmKiZGKUYmRitGKkYmKihJImFHRiVGJkYpRiZGK0YmRiYqJkYuRiZGKUYqRiYqJkYpRiZGLkYqRiYqJkYrRiZGLkYqRiYqJkYuRiZGK0YqRiZGJkYuISIiRilGM0YrRjMjRiZGKg== rad2:= (factor@subs)(defR2, apol_rad^2); ; LCQqLCwoSSJiRzYiIiIiSSJhR0YmRidJImNHRiYhIiJGKiwoRihGJ0YlRidGKUYnRiosKEYoRidGKUYnRiVGKkYqLChGJUYqRilGKkYoRidGKiwwKiZGJSIiI0YpRidGJyomRiVGJ0YpRjBGJyooRihGJ0YlRidGKUYnRicqJkYoRidGJUYwRicqJkYlRidGKEYwRicqJkYpRidGKEYwRicqJkYoRidGKUYwRidGMCNGKiIiJQ== # ruleW:= WW3^2=W3^2; (factor@pp2uu)(cent): apol_uu:= (Vector@factor@subs)(defR2,%); ici_uu:=%: ency(%); LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpJXleKFI= SSI/RzYi subs(rho2=rad2, valR22, zipq(Vector(pu), ici_uu), eq_dou): eqn0:= sort(collect(%, px, factor, distributed), [x,y,z]); 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 circlefunction:= subs(y=0,z=0,x=1,eqn0)/b/c; facxx, facyz:=(a+b+c)/4, 1/2 : j:='j': A(facxx)*Sum( factor(coeff(eqn0,x,2)/facxx)*x^2,j)+ A(facyz)*Sum(factor(coeff(coeff(eqn0,y),z)/facyz)*y*z,j): ici_eqn:= sort(%, [a,b,c,x,y,z]); LCYqJi1JIkFHNiI2IywoSSJhR0YmIyIiIiIiJUkiYkdGJkYqSSJjR0YmRipGKy1JJFN1bUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJjYkKigsKiokRikiIiNGKyomRilGK0YtRitGKyomRilGK0YuRitGKyomRi1GK0YuRitGOEYrRikhIiJJInhHRiZGOEkiakdGJkYrRisqJi1GJTYjI0YrRjhGKy1GMDYkKiwsNiomRilGOEYtRjhGKyooRilGOEYtRitGLkYrIiIkKiZGKUY4Ri5GOEYrKiZGKUYrRi1GSUYrKihGKUYrRi1GOEYuRitGSSooRilGK0YtRitGLkY4RkkqJkYpRitGLkZJRisqJkYtRklGLkYrRisqJkYtRjhGLkY4RjgqJkYtRitGLkZJRitGK0YtRjxGLkY8SSJ5R0YmRitJInpHRiZGK0Y+RitGKw== (factor@mm2persp@eq2mm)(eqn0): ici_persp:= elimifacu(%); ency(%); 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 SSI/RzYi tmp_inv:= bary2norm(cent)+(bary2norm(px)-bary2norm(cent))*rad2/(rad2-eqn0/(x+y+z)^2): #tmq:= (reduce@factor@evalmm)(%): (Vector@factor@subs)(defR2, %): #collect(-%/rotp(a^2), px, normal@expand, distributed); les fonctions funon, funinv, funsym (reduce@factor@evalmm@subs)(ency_, tmp_inv): funinv:= unapply(%,x,y,z)@op: funon:= unapply(subs(ency_, eqn0), x,y,z)@op: (reduce@subs)(ency_, reflection(cent,px)): funsym:= unapply(%,x,y,z)@op: Bien r\303\251gler le seuil... ou bien passer \303\240 20 chiffres Digits:=20: ici_on:= [seq](`if`((abs@funon)(xyz[j])<Float(1,-6),j,NULL),j=1..jmax); nops(%); NyoiJVA/IiVRPyIlSEkiJUlJIiVKSSIlS0kiJUxJIiVNSQ== IiIp Les inverses-in-circle qqr:= table(): for j to jmax do if ff[j]=1 then next fi; tmp:= ency(funinv(xyz[j])): if tmp <>`?` then qqr[j]:= tmp; fi; od: # j:='j': ici_inv:= sort(map(op,[indices](qqr))); nops(%); bad_points=seq(`if`(qqr[qqr[j]]=j,NULL,j), j=ici_inv); NyoiJVA/IiVRPyIlSEkiJUlJIiVKSSIlS0kiJUxJIiVNSQ== IiIp L0krYmFkX3BvaW50c0c2IkYk On doit retrouver le nombre de points sur le cercle [seq](`if`(qqr[j]=j,j,NULL),j=ici_inv): nops(%); IiIp Les antipodaux qqr:= table(): for j in ici_on do tmp:= ency(funsym(xyz[j])): if tmp <>`?` then qqr[j]:= tmp; fi; od: j:='j': lesk:= sort(map(op,[indices](qqr))); nops(%); bad_points=seq(`if`(qqr[qqr[j]]=j,NULL,j), j=lesk); NyQiJVA/IiVRPw== IiIj L0krYmFkX3BvaW50c0c2IkYk Digits:=10: Il faut envoyer cela ***si besoin*** dans un r\303\251pertoire lisible et navigable if false then try close(fd); catch : end try; fd := open("/home/douillet/public_html/etc/alt_data.csv", WRITE): for j in lesk do fprintf(fd, """%d"";""%d""\134n", j, qqr[j]); od: close(fd); j:='j': fi:
<Text-field style="Heading 1" layout="Heading 1">Les antipodes-- apollonius</Text-field> _O1:= pX(3); _O2:= pX(970); _U:= pX(573); _V:= pX(386); NyUqJilJImFHNiIiIiMiIiIsKCokKUkiYkdGJkYnRihGKCokKUkiY0dGJkYnRihGKCokRiRGKCEiIkYoKiZGK0YoLChGLUYoRjBGKEYqRjFGKComRi5GKCwoRjBGKEYqRihGLUYxRig= 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 NyUqJilJImFHNiIiIiMiIiIsKiomLCZJImNHRiZGKEkiYkdGJkYoRihGJEYoRigqKEYlRihGLUYoRixGKCEiIiokKUYtIiIkRihGLyokKUYsRjJGKEYvRigqJilGLUYnRigsKiomLCZGJUYoRixGKEYoRjZGKEYoRi5GL0YzRi8qJClGJUYyRihGL0YoKiYpRixGJ0YoLCoqJiwmRi1GKEYlRihGKEY9RihGKEYuRi9GOkYvRjBGL0Yo NyUqJilJImFHNiIiIiMiIiIsKiomRiVGKCwmSSJjR0YmRihJImJHRiZGKEYoRigqJClGLUYnRihGKComRi1GKEYsRihGKCokKUYsRidGKEYoRigqJkYvRigsKiomRi1GKCwmRiVGKEYsRihGKEYoRjFGKComRixGKEYlRihGKCokRiRGKEYoRigqJkYyRigsKiomRixGKCwmRi1GKEYlRihGKEYoRjhGKComRiVGKEYtRihGKEYuRihGKA== harmo(_O1,_O2,_U,_V); ISIi _P:= pp; _PP:= collect(reflection(_O1,pp), pp, factor); NyVJInBHNiJJInFHRiRJInJHRiQ= NyUsKCooLCgqJClJImNHNiIiIiMiIiJGKyokKUkiYUdGKUYqRitGKyokKUkiYkdGKUYqRishIiJGKywoRixGK0YvRitGJkYyRitJInBHRilGK0YyKipGKkYrRi1GKywoRi9GMkYmRjJGLEYrRitJInFHRilGK0YyKipGKkYrRi1GK0Y2RitJInJHRilGK0YyLCgqKkYqRitGMEYrRiVGK0Y0RitGKyooRjNGK0Y2RitGN0YrRisqKkYqRitGMEYrRiVGK0Y5RitGKywoKipGKkYrRidGK0YzRitGNEYrRisqKkYqRitGJ0YrRjNGK0Y3RitGKyooRiVGK0Y2RitGOUYrRis= (reduce@factor@wedge)(wedge(_P,_U),wedge(_PP,_V)): collect(%, pp, factor): _Q:= Vector(xcollect(%, [rot3](a^2*b+a^2*c-a*b*c-b^3-c^3), factor )); 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 (elimifacu@factor@wedge)(wedge(_PP,_U),wedge(_P,_V)); collect(%, pp, factor): _QQ:= Vector(xcollect(-%, [rot3](a*b+a*c+b^2+b*c+c^2), factor)); LUkjbXNHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2I1ElZmluaUYn 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 LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIwdyhINzFtMTk= On teste l'antipodie (reduce@factor)(bary2norm(_Q)+bary2norm(_QQ)): zipd(%, _O2); NyUhIiJGI0Yj fac:=a^2: subs(zipq(pp, prm_cir(pdr)), _Q): %[1]: map(U-> U/fac, op(1,%))*fac*op(2,%)/(a+b+c): _Qprm:= Vector([rot3](%)); 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 fac:=a^2: subs(zipq(pp, prm_cir(pdr)), _QQ): %[1]: map(U-> U/fac, op(1,%))*fac*op(2,%)/rotp(a+b): _QQprm:= Vector([rot3](%)); 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 kic:= [rot3]((b^2/(-rho+tau)+c^2/(rho-sigma))/(sigma-tau)); NyUqJiwmKiYpSSJiRzYiIiIjIiIiLCZJJHJob0dGKCEiIkkkdGF1R0YoRipGLUYqKiYpSSJjR0YoRilGKiwmRixGKkkmc2lnbWFHRihGLUYtRipGKiwmRjNGKkYuRi1GLSomLCYqJilJImFHRihGKUYqRjRGLUYqRi9GKkYqRitGLSomLCZGN0YqRiVGKkYqRjJGLQ== barydiv(_QQprm, kic); ency(%); NyUsJComLCwqJkkiYUc2IiIiIkkiYkdGKEYpRikqJkkiY0dGKEYpRidGKUYpKiQpRioiIiNGKUYpKiQpRixGL0YpRikqJkYqRilGLEYpRilGKSwmRixGKUYqRilGKSEiIiwkKiYsLEYyRilGK0YpRjBGKSokKUYnRi9GKUYpRiZGKUYpLCZGJ0YpRixGKUYpRjQsJComLCxGK0YpRi1GKUY4RilGMkYpRiZGKUYpLCZGKkYpRidGKUYpRjQ= SSI/RzYi
<Text-field style="Heading 1" layout="Heading 1">Les antipodes-- spieker</Text-field> _O1:= pX(3); _O2:= pX(10); _U:= pX(958); _V:= pX(1376); NyUqJilJImFHNiIiIiMiIiIsKCokKUkiYkdGJkYnRihGKCokKUkiY0dGJkYnRihGKCokRiRGKCEiIkYoKiZGK0YoLChGLUYoRjBGKEYqRjFGKComRi5GKCwoRjBGKEYqRihGLUYxRig= NyUsJkkiY0c2IiIiIkkiYkdGJUYmLCZJImFHRiVGJkYkRiYsJkYnRiZGKUYm NyUqKEkiYUc2IiIiIiwoSSJiR0YlRiZGJCEiIkkiY0dGJUYmRiYsKCokKUYkIiIjRiZGJiomRiRGJiwmRipGJkYoRiZGJkYmKihGLkYmRihGJkYqRiZGJkYmKihGKEYmLChGKkYmRiRGJkYoRilGJiwoKiQpRihGLkYmRiYqJkYoRiYsJkYkRiZGKkYmRiZGJiooRi5GJkYqRiZGJEYmRiZGJiooRipGJiwoRihGJkYkRiZGKkYpRiYsKCokKUYqRi5GJkYmKiZGKkYmLCZGKEYmRiRGJkYmRiYqKEYuRiZGJEYmRihGJkYmRiY= NyUqJkkiYUc2IiIiIiwqKiQpRiQiIiNGJkYmKiZGJEYmSSJiR0YlRiYhIiIqJkkiY0dGJUYmRiRGJkYtKihGKkYmRixGJkYvRiZGJkYmKiZGLEYmLCoqJClGLEYqRiZGJiomRixGJkYvRiZGLUYrRi0qKEYqRiZGL0YmRiRGJkYmRiYqJkYvRiYsKiokKUYvRipGJkYmRi5GLUY1Ri0qKEYqRiZGJEYmRixGJkYmRiY= harmo(_O1,_O2,_U,_V); ISIi _P:= pp; _PP:= collect(reflection(_O1,pp), pp, factor); NyVJInBHNiJJInFHRiRJInJHRiQ= NyUsKCooLCgqJClJImNHNiIiIiMiIiJGKyokKUkiYUdGKUYqRitGKyokKUkiYkdGKUYqRishIiJGKywoRixGK0YvRitGJkYyRitJInBHRilGK0YyKipGKkYrRi1GKywoRi9GMkYmRjJGLEYrRitJInFHRilGK0YyKipGKkYrRi1GK0Y2RitJInJHRilGK0YyLCgqKkYqRitGMEYrRiVGK0Y0RitGKyooRjNGK0Y2RitGN0YrRisqKkYqRitGMEYrRiVGK0Y5RitGKywoKipGKkYrRidGK0YzRitGNEYrRisqKkYqRitGJ0YrRjNGK0Y3RitGKyooRiVGK0Y2RitGOUYrRis= (reduce@factor@wedge)(wedge(_P,_U),wedge(_PP,_V)): collect(%, pp, factor): _Q:= Vector(xcollect(%, [ rot3(b+c-a), rot3(a^2+a*b+a*c+2*b*c)], factor )); 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 (elimifacu@factor@wedge)(wedge(_PP,_U),wedge(_P,_V)); collect(%, pp, factor): _QQ:= Vector(xcollect(-%, [ rot3(a^2-a*b-a*c+2*b*c)], factor)); LUkjbXNHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2I1ElZmluaUYn 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 LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpRzB0Xw== On teste l'antipodie (reduce@factor)(bary2norm(_Q)+bary2norm(_QQ)): zipd(%, _O2); NyUiIiJGI0Yj fac:=a^2: subs(zipq(pp, prm_cir(pdr)), _Q): %[1]: map(U-> U/fac, op(1,%))*fac*op(2,%): _Qprm:= Vector([rot3](%)); 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 fac:=a^2: subs(zipq(pp, prm_cir(pdr)), _QQ): %[1]: map(U-> U/fac, op(1,%))*fac*op(2,%): _QQprm:= Vector([rot3](%)); 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 kic:= [rot3]((b^2/(-rho+tau)+c^2/(rho-sigma))/(sigma-tau)); NyUqJiwmKiYpSSJiRzYiIiIjIiIiLCZJJHJob0dGKCEiIkkkdGF1R0YoRipGLUYqKiYpSSJjR0YoRilGKiwmRixGKkkmc2lnbWFHRihGLUYtRipGKiwmRjNGKkYuRi1GLSomLCYqJilJImFHRihGKUYqRjRGLUYqRi9GKkYqRitGLSomLCZGN0YqRiVGKkYqRjJGLQ== barydiv(_QQprm, kic); ency(%); NyUqKEkiYUc2IiEiIiwqKiQpRiQiIiMiIiJGKyomRiRGK0kiYkdGJUYrRiYqJkkiY0dGJUYrRiRGK0YmKihGKkYrRi1GK0YvRitGK0YrLC4qJkYkRispRi9GKkYrRisqJkYkRispRi1GKkYrRisqJClGLyIiJEYrRiYqJClGLUY4RitGJiomRi9GK0Y1RitGKyomRi1GK0YzRitGK0YrKihGLUYmLCoqJEY1RitGKyomRi1GK0YvRitGJkYsRiYqKEYqRitGL0YrRiRGK0YrRissLiomRi1GK0YpRitGK0Y8RisqJClGJEY4RitGJkY2RiZGMkYrKiZGL0YrRilGK0YrRisqKEYvRiYsKiokRjNGK0YrRi5GJkZARiYqKEYqRitGJEYrRi1GK0YrRissLkY7RitGRkYrRjlGJkZERiZGQ0YrRjRGK0Yr SSI/RzYi
jmax; IiU5Tg== 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KEZORi1GS0YtRkxGLUY1RixGPEZFRk5GLkY5RkJGS0YxRjpGQ0ZMRiY=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TTdSMApJNVJUQUJMRV9TQVZFLzE5NTc3OTIwWCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjKiIkIiQsLiokJSJiRyIiIyIiIiomRilGKyUiY0dGK0YqKiYlImFHRitGKUYrISIjKiRGLUYqRisqJkYvRitGLUYrRjAqJEYvRipGKywqRi5GMEYoRitGMSEiIkYzRissKkYoRjVGMkYwRjFGK0YzRitGNCwuRjNGK0YyRipGLkYwRjFGK0YsRjBGKEYrLCpGLEYwRjFGK0YoRitGM0Y1RjZGOCwuRihGK0YuRipGLEYwRjNGK0YyRjBGMUYrRiY=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TTdSMApJNFJUQUJMRV9TQVZFLzYxMDY3MjBYKiUpYW55dGhpbmdHNiI2IltnbCEjJSEhISIkIiQsJComJSJhRyIiIywoKiZGKUYqJSRyaG9HIiIiRioqJiwoKiRGKUYqISIiKiQlImJHRipGMiokJSJjR0YqRi5GLiUmc2lnbWFHRi5GLiomLChGNUYyRjFGMkYzRi5GLiUkdGF1R0YuRi5GMkYyKiZGNEYqLCgqJiwoRjFGLkYzRi5GNUYyRi5GLUYuRi4qJkY0RipGN0YuISIjKiYsKEYxRjJGM0YuRjVGLkYuRjpGLkYuRjIqJkY2RiosKComLChGNUYuRjFGLkYzRjJGLkYtRi5GLiomRkJGLkY3Ri5GLiomRjZGKkY6Ri5GQEYyRiY=TTdSMApJNFJUQUJMRV9TQVZFLzU0NDYxMjBYKiUpYW55dGhpbmdHNiI2IltnbCEjJSEhISIkIiQqJCUiUkciIiNGJ0YnRiY=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TTdSMApJNVJUQUJMRV9TQVZFLzM5OTY5NDcyWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkKiYsKComLCYlImJHIiIiJSJjRyEiIiIiIyUicEdGLEYsKiYlImFHRi8lInFHRixGLComJSJyR0YsRjJGL0YsRiwsKEYrRixGLUYsRjJGLkYsKiYsKComRjBGLEYrRi9GLComLCZGMkYsRi1GLkYvRjNGLEYsKiZGNUYsRitGL0YsRiwsKEYyRixGLUYsRitGLkYsKiYsKComRjBGLEYtRi9GLComRi1GL0YzRixGLComLCZGMkYsRitGLkYvRjVGLEYsRiwsKEYrRixGMkYsRi1GLkYsRiY=TTdSMApJNVJUQUJMRV9TQVZFLzQwMzIzNzI4WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkKiYsKComLCYlImJHIiIiJSJjR0YsIiIjJSJwR0YsRiwqJiUiYUdGLiUicUdGLEYsKiYlInJHRixGMUYuRixGLCwoRitGLEYtRixGMSEiIkY2KiYsKComRi9GLEYrRi5GLComLCZGMUYsRi1GLEYuRjJGLEYsKiZGNEYsRitGLkYsRiwsKEYxRixGLUYsRitGNkY2KiYsKComRi9GLEYtRi5GLComRi1GLkYyRixGLComLCZGK0YsRjFGLEYuRjRGLEYsRiwsKEYrRixGMUYsRi1GNkY2RiY=TTdSMApJNVJUQUJMRV9TQVZFLzUxMTAxNDQwWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkKigsKComLCYlImJHIiIiJSJjRyEiIiIiIywmJSZzaWdtYUdGLCUkdGF1R0YuRi5GLComRitGLywmJSRyaG9HRi5GMkYsRi5GLComRi1GLywmRjVGLEYxRi5GLkYsRiwlImFHRi8sKEYrRixGLUYsRjhGLkYsKigsKComLCZGLUYsRjhGLkYvRjRGLkYsRjZGLComRjhGL0YwRi5GLEYsRitGLywoRjhGLEYtRixGK0YuRiwqKCwoKiYsJkY4RixGK0YuRi9GN0YuRixGPkYsRjNGLEYsRi1GLywoRitGLEY4RixGLUYuRixGJg==TTdSMApJNVJUQUJMRV9TQVZFLzQ1OTU4MzM2WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkKigsKComLCYlImJHIiIiJSJjR0YsIiIjLCYlJnNpZ21hR0YsJSR0YXVHISIiRjJGLComRitGLiwmJSRyaG9HRjJGMUYsRjJGLComRi1GLiwmRjVGLEYwRjJGMkYsRiwlImFHRi4sKEYrRixGLUYsRjhGMkYyKigsKComLCZGOEYsRi1GLEYuRjRGMkYsRjZGLComRjhGLkYvRjJGLEYsRitGLiwoRjhGLEYtRixGK0YyRjIqKCwoKiYsJkYrRixGOEYsRi5GN0YyRixGPkYsRjNGLEYsRi1GLiwoRitGLEY4RixGLUYyRjJGJg==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TTdSMApJNVJUQUJMRV9TQVZFLzE1MTI1ODE2WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkKiosMComJSJhRyIiIyUiYkciIiVGKyooRipGK0YsRislImNHRisiIiYqJkYqRitGL0YtRisqJEYsIiInISIiKiZGLEYtRi9GKyIiIiomRixGK0YvRi1GNiokRi9GM0Y0RjYsKCokRipGK0Y2KiRGLEYrRjYqJEYvRitGNiEiIyUiUkdGK0YqRj0sJCoqLDAqJEYqRjNGNiomRipGLUYsRitGPSomRipGLUYvRitGNEYuISImRjFGNEY3Rj1GOEY2RjZGOUY9Rj5GK0YsRj1GNCwkKiosMEZCRjZGQ0Y0RkRGPUYpRjRGLkZFRjJGNkY1Rj1GNkY5Rj1GPkYrRi9GPUY0RiY=TTdSMApJNVJUQUJMRV9TQVZFLzM5NjczMDMyWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkLCQqJiwuKiQlImFHIiIkIiIiKiZGK0YtJSJjRyIiIyEiIyomRitGLSUiYkdGMEYxKihGK0YtRjNGLUYvRi1GLSokRi9GLCEiIiokRjNGLEY2Ri0sKEYrRi1GM0YtRi9GLUY2I0Y2IiIlLCQqJiwuRipGLSomRitGMEYzRi1GMEY0RjZGN0Y2RjVGLSomRjNGLUYvRjBGMEYtRjhGNiNGLUY6LCQqJiwuRipGLSomRitGMEYvRi1GMEY0RjYqJkYzRjBGL0YtRjBGN0YtRjVGNkYtRjhGNkZARiY=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TTdSMApJNVJUQUJMRV9TQVZFLzI0NDQxODU2WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkLCQqKiUiYkciIiMlImNHRiosKCokJSJhR0YqIiIiKiRGK0YqISIjKiRGKUYqRjFGLywoRi1GL0YyRi9GMEYvRjEhIiIqKkYuRipGK0YqLChGLUYqRjJGNEYwRipGL0YzRjEqKkYuRipGKUYqLChGMkYqRi1GKkYwRjRGL0YzRjFGJg==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